corporate finance modeling

8/14/2019 Corporate Finance Modeling

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PROJECT NPV Sensitivity Analysis(In Thouands of $) 2009 2010 2011 2012

Year 0 Year 1 Year 2 Year 3

Key Assumptions

Unit Sales 2000 4000 5600

Inflation Rate 2.00% 2.50% 3.00%Real Cost of Capital 11.00% 11.20% 11.40%

Tax Rate 35.00% 35.00% 35.00%

Discounting

Discount Rate = Cost of Capital 13.22% 13.98% 14.74%

Cumulative Discount Factor 13.22% 29.05% 48.07%

Price or Cost / Unit

Sales Revenue / Unit $9.70 $9.94 $10.24

Variable Cost / Unit

Direct Labor $3.50 $3.59 $3.70

Materials $2.00 $2.05 $2.11

Selling Expenses $1.20 $1.23 $1.27

Others $0.70 $0.72 $0.74

Total Variable Cost / Unit $7.40 $7.59 $7.81

Cash Fixed Costs:

Lease Payment $2,800.00 $2,870.00 $2,956.10

Property Taxes $580.00 $594.50 $612.34

Administration $450.00 $461.25 $475.09

Advertising $930.00 $953.25 $981.85

Other $520.00 $533.00 $548.99

Total Cash Fixed Cost $5,280.00 $5,412.00 $5,574.36

Working Cap / Next Yr Unit Sales $0.87 $0.89 $0.91 $0.94

Working Capital $1,740.00 $3,549.60 $5,093.68 $6,370.73

Cash Flow Forecasts

Sales Revenue $19,400.00 $39,770.00 $57,348.34

Variable Costs $14,800.00 $30,340.00 $43,750.28

Gross Margin $4,600.00 $9,430.00 $13,598.06

Cash Fixed Costs $5,280.00 $5,412.00 $5,574.00

Depreciation $1,621.43 $1,621.43 $1,621.43

Total Fixed Costs $6,901.43 $7,033.43 $7,195.43

Operating Profit $(2,301.43) $2,396.57 $6,402.63

Taxes $(805.50) $838.80 $2,240.92

Net Profit $(1,495.93) $1,557.77 $4,161.71

Add Back Depreciation $1,621.43 $1,621.43 $1,621.43

Operating Cash Flow $125.50 $3,179.20 $5,783.14

Investment in Working Capital $(1,740.00) $(1,809.60) $(1,544.08) $(1,277.06)


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Investment in Plant & Equipment $(11,350.00)

Cash Flow $(13,090.00) $(1,809.60) $(1,544.08) $(1,277.06)

Cash Flows $(13,090.00) $(1,684.10) $1,635.12 $4,506.08

Present Value of Each Cash Flow $(13,090.00) $(1,487.46) $1,267.06 $3,043.16

Net Present Value $3,468.53

Data Table: Sensitivity of the Project NPV to Unit Sales and the Real Cost of Capital

Input Values for Unit Sales Scale Factor

Output Formula: Proj NPV $3,468.53 80.00% 90.00% 100.00%

9.00%

Input Values for Date 0 Real Cost of Capital 11.00%

13.00%

15.00%

17.00%


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2013 2014 2015 2016


6800 7400 3700 1800

3.50% 4.00% 4.00% 4.00%11.60% 11.80% 12.00% 12.20%

35.00% 35.00% 35.00% 35.00%

15.51% 16.27% 16.48% 16.69%

71.03% 98.86% 131.64% 170.29%

$10.60 $11.02 $11.46 $11.92

$3.82 $3.98 $4.14 $4.30

$2.19 $2.27 $2.36 $2.46

$1.31 $1.36 $1.42 $1.47

$0.76 $0.80 $0.83 $0.86

$8.09 $8.41 $8.75 $9.10

$3,059.56 $3,181.95 $3,309.22 $3,441.59

$633.77 $659.12 $685.48 $712.90

$491.72 $511.38 $531.84 $553.11

$1,016.21 $1,056.86 $1,099.14 $1,143.10

$568.20 $590.93 $614.57 $639.15

$5,769.46 $6,000.24 $6,240.25 $6,489.86

$0.97 $1.01 $1.05 $1.09

$7,175.51 $3,731.26 $1,887.82 $-

$72,074.57 $81,571.46 $42,417.16 $21,460.79

$54,984.73 $62,229.77 $32,359.48 $16,372.15

$17,089.85 $19,341.69 $10,057.68 $5,088.64

$5,789.00 $6,000.00 $6,240.00 $6,490.00

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,410.43 $7,621.43 $7,861.43 $8,111.43

$9,679.42 $11,720.26 $2,196.25 $(3,022.79)

$3,387.80 $4,102.09 $768.69 $(1,057.98)

$6,291.62 $7,618.17 $1,427.56 $(1,964.81)

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,913.05 $9,239.60 $3,048.99 $(343.38)

$(804.77) $3,444.24 $1,843.45 $1,887.82


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$1,400.00

$(804.77) $3,444.24 $1,843.45 $3,287.82

$7,108.28 $12,683.84 $4,892.44 $2,944.43

$4,156.10 $6,378.18 $2,112.13 $1,089.36

110.00% 120.00%


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PROJECT NPV Working Capital(In Thouands of $) 2009 2010 2011 2012


Key Assumptions

Unit Sales 2000 4000 5600


Tax Rate 35.00% 35.00% 35.00%

Discounting






Direct Labor $3.50 $3.59 $3.70

Materials $2.00 $2.05 $2.11


Others $0.70 $0.72 $0.74


Cash Fixed Costs:

Lease Payment $2,800.00 $2,870.00 $2,956.10

Property Taxes $580.00 $594.50 $612.34

Administration $450.00 $461.25 $475.09

Advertising $930.00 $953.25 $981.85

Other $520.00 $533.00 $548.99


Working Cap / Next Yr Unit Sales $0.87 $0.89 $0.91 $0.94

Working Capital $1,740.00 $3,549.60 $5,093.68 $6,370.73

Cash Flow Forecasts

Sales Revenue $19,400.00 $39,770.00 $57,348.34

Variable Costs $14,800.00 $30,340.00 $43,750.28

Gross Margin $4,600.00 $9,430.00 $13,598.06

Cash Fixed Costs $5,280.00 $5,412.00 $5,574.00

Depreciation $1,621.43 $1,621.43 $1,621.43



Taxes $(805.50) $838.80 $2,240.92

Net Profit $(1,495.93) $1,557.77 $4,161.71



Investment in Working Capital $(1,740.00) $(1,809.60) $(1,544.08) $(1,277.06)


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Cash Flow $(13,090.00) $(1,809.60) $(1,544.08) $(1,277.06)

Cash Flows $(13,090.00) $(1,684.10) $1,635.12 $4,506.08

Present Value of Each Cash Flow $(13,090.00) $(1,487.46) $1,267.06 $3,043.16



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2013 2014 2015 2016


6800 7400 3700 1800

3.50% 4.00% 4.00% 4.00%11.60% 11.80% 12.00% 12.20%

35.00% 35.00% 35.00% 35.00%

15.51% 16.27% 16.48% 16.69%

71.03% 98.86% 131.64% 170.29%

$10.60 $11.02 $11.46 $11.92

$3.82 $3.98 $4.14 $4.30

$2.19 $2.27 $2.36 $2.46

$1.31 $1.36 $1.42 $1.47

$0.76 $0.80 $0.83 $0.86

$8.09 $8.41 $8.75 $9.10

$3,059.56 $3,181.95 $3,309.22 $3,441.59

$633.77 $659.12 $685.48 $712.90

$491.72 $511.38 $531.84 $553.11

$1,016.21 $1,056.86 $1,099.14 $1,143.10

$568.20 $590.93 $614.57 $639.15

$5,769.46 $6,000.24 $6,240.25 $6,489.86

$0.97 $1.01 $1.05 $1.09

$7,175.51 $3,731.26 $1,887.82 $-

$72,074.57 $81,571.46 $42,417.16 $21,460.79

$54,984.73 $62,229.77 $32,359.48 $16,372.15

$17,089.85 $19,341.69 $10,057.68 $5,088.64

$5,789.00 $6,000.00 $6,240.00 $6,490.00

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,410.43 $7,621.43 $7,861.43 $8,111.43

$9,679.42 $11,720.26 $2,196.25 $(3,022.79)

$3,387.80 $4,102.09 $768.69 $(1,057.98)

$6,291.62 $7,618.17 $1,427.56 $(1,964.81)

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,913.05 $9,239.60 $3,048.99 $(343.38)

$(804.77) $3,444.24 $1,843.45 $1,887.82


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$1,400.00

$(804.77) $3,444.24 $1,843.45 $3,287.82

$7,108.28 $12,683.84 $4,892.44 $2,944.43

$4,156.10 $6,378.18 $2,112.13 $1,089.36


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PROJECT NPV Forecasting Cash Flow(In Thouands of $) 2009 2010 2011 2012


Key Assumptions

Unit Sales 2000 4000 5600


Tax Rate 35.00% 35.00% 35.00%

Discounting






Direct Labor $3.50 $3.59 $3.70

Materials $2.00 $2.05 $2.11


Others $0.70 $0.72 $0.74


Cash Fixed Costs:

Lease Payment $2,800.00 $2,870.00 $2,956.10

Property Taxes $580.00 $594.50 $612.34

Administration $450.00 $461.25 $475.09

Advertising $930.00 $953.25 $981.85

Other $520.00 $533.00 $548.99



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2013 2014 2015 2016


6800 7400 3700 1800

3.50% 4.00% 4.00% 4.00%11.60% 11.80% 12.00% 12.20%

35.00% 35.00% 35.00% 35.00%

15.51% 16.27% 16.48% 16.69%

71.03% 98.86% 131.64% 170.29%

$10.60 $11.02 $11.46 $11.92

$3.82 $3.98 $4.14 $4.30

$2.19 $2.27 $2.36 $2.46

$1.31 $1.36 $1.42 $1.47

$0.76 $0.80 $0.83 $0.86

$8.09 $8.41 $8.75 $9.10

$3,059.56 $3,181.95 $3,309.22 $3,441.59

$633.77 $659.12 $685.48 $712.90

$491.72 $511.38 $531.84 $553.11

$1,016.21 $1,056.86 $1,099.14 $1,143.10

$568.20 $590.93 $614.57 $639.15

$5,769.46 $6,000.24 $6,240.25 $6,489.86


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PROJECT NPV Basics(In Thouands of $) 2009 2010 2011 2012


Key Assumptions

Unit Sales 2000 4000 5600


Tax Rate 35.00% 35.00% 35.00%

Discounting





Variable Cost / Unit $7.40 $7.59 $7.81

Cash Fixed Costs $5,280.00 $5,412.00 $5,574.00

Cash Flow Forecasts

Sales Revenue $19,400.00 $39,770.00 $57,348.34

Variable Costs $14,800.00 $30,340.00 $43,750.28

Gross Margin $4,600.00 $9,430.00 $13,598.06

Cash Fixed Costs $5,280.00 $5,412.00 $5,574.00

Depreciation $1,621.43 $1,621.43 $1,621.43



Taxes $(805.50) $838.80 $2,240.92

Net Profit $(1,495.93) $1,557.77 $4,161.71




Cash Flow $(11,350.00) $125.50 $3,179.20 $5,783.14

Present Value of Each Cash Flow $(11,350.00) $110.85 $2,463.58 $3,905.61



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2013 2014 2015 2016


6800 7400 3700 1800

3.50% 4.00% 4.00% 4.00%11.60% 11.80% 12.00% 12.20%

35.00% 35.00% 35.00% 35.00%

15.51% 16.27% 16.48% 16.69%

71.03% 98.86% 131.64% 170.29%

$10.60 $11.02 $11.46 $11.92

$8.09 $8.41 $8.75 $9.10

$5,789.00 $6,000.00 $6,240.00 $6,490.00

$72,074.57 $81,571.46 $42,417.16 $21,460.79

$54,984.73 $62,229.77 $32,359.48 $16,372.15

$17,089.85 $19,341.69 $10,057.68 $5,088.64

$5,789.00 $6,000.00 $6,240.00 $6,490.00

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,410.43 $7,621.43 $7,861.43 $8,111.43

$9,679.42 $11,720.26 $2,196.25 $(3,022.79)

$3,387.80 $4,102.09 $768.69 $(1,057.98)

$6,291.62 $7,618.17 $1,427.56 $(1,964.81)

$1,621.43 $1,621.43 $1,621.43 $1,621.43

$7,913.05 $9,239.60 $3,048.99 $(343.38)

$1,400.00

$7,913.05 $9,239.60 $3,048.99 $1,056.62

$4,626.63 $4,646.21 $1,316.29 $390.92


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THE YIELD CURVE - Using it to Determine Forward RateMaturity Time to Yield to Forward

Inputs Date Maturity Maturity Rates

Today 07/07/09

One month Treasury Bill 08/07/09 0.09 3.96% 3.96%

Three month Treasury Bill 10/04/09 0.24 5.19% 5.86%Six month Treasury Bill 01/03/10 0.49 5.43% 5.67%

One year Treasury Bill 07/07/10 1.00 5.78% 6.12%

Two Year Investment Bond 07/07/11 2.00 5.94% 6.10%

Three Year Investment Bond 07/06/12 3.00 5.99% 6.10%

Four Year Investmetn Bond 07/06/13 4.00 6.05% 6.22%

Five Year Investment Bond 07/06/14 5.00 6.26% 7.10%

Ten Year Investment Bond 07/06/19 10.00 6.56% 6.86%

Fifteen Year Investment Bond 07/06/24 15.00 6.59% 6.65%

Twenty Year Investment Bond 07/07/29 20.00 6.54% 6.39%

Twenty Five Year Investment Bond 07/05/34 24.99 6.34% 5.54%

Thrity Year Investment Bond 07/07/39 30.00 6.08% 4.79%

0.09 0.24 0.49 1.00 2.00 3.00 4.00 5.00 10.00 15.00 20.00 24.99 30.00

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

5.00%

5.50%

6.00%

6.50%

7.00%

7.50%

U.S. Treasury Zero - Coupon Yield Curve

Column D

Column E

Time to Maturity (Years)

Yield

toMaturity(Annual)


14/54

THE YIELD CURVE - Obtaining it from Bond ListingsMaturity Time to Yield to

Inputs Date Maturity Maturity

Today 07/07/09

One month Treasury Bill 08/07/09 0.09 12.50%

Three month Treasury Bill 10/04/09 0.24 12.95%Six month Treasury Bill 01/03/10 0.49 13.00%

One year Treasury Bill 07/07/10 1.00 13.25%

Two Year Investment Bond 07/07/11 2.00 13.50%

Three Year Investment Bond 07/06/12 3.00 13.88%

Four Year Investmetn Bond 07/06/13 4.00 14.00%

Five Year Investment Bond 07/06/14 5.00 14.34%

Seven Year Investment Bond 07/06/16 7.00 14.70%

Ten Year Investment Bond 07/06/19 10.00 14.86%

Fifteen Year Investment Bond 07/06/24 15.00 15.36%

Twenty Year Investment Bond 07/07/29 20.00 15.70%

Twenty Five Year Investment Bond 07/05/34 24.99 16.00%

Thrity Year Investment Bond 07/07/39 30.00 16.22%

Bond Inputs

Rate Convention: 1=EAR, 0=APR 1 Effective Annual Rate

Annual Coupon Rate (CR) 12.00%

Number of Payments / Year (NOP) 1

Number of Periods to Maturity (N) 10

Face Value (M) $1,000.00

Outputs

Coupon Payment (INT) $120.00

Calculate the Price and Yield to Maturity of a Coupon Bond using the Cash Flows

Period 0 1 2 3

Time (Years) 0 1 2 3

Cash Flows $120.00 $120.00 $120.00

Yield to Maturity (Annualized) 12.50% 12.95% 13.00%

Discount Rate / Period 12.50% 12.95% 13.00%

Present Value of Cash Flow $106.67 $94.06 $83.17

Coupon Bond Price $867.52

Coupon Bond Discount Rate / Period 14.60%

Coupon Bond Yield to Maturity 14.60%

12.25%

12.50%

12.75%

13.00%

13.25%

13.50%

13.75%

14.00%

14.25%

14.50%

14.75%15.00%

15.25%

15.50%

15.75%

16.00%

16.25%

YieldtoMaturity(Annual)


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4 5 6 7 8 9 10

4 5 6 7 8 9 10

$120.00 $120.00 $120.00 $120.00 $120.00 $120.00 $1,120.00

13.25% 13.50% 13.88% 14.00% 14.34% 14.86% 15.36%

13.25% 13.50% 13.88% 14.00% 14.34% 14.86% 15.36%

$72.95 $63.71 $55.02 $47.96 $41.09 $34.48 $268.43

- 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00

Treasury Coupon Yield Curve



16/54

THE YIELD CURVE - Obtaining it from Bond ListingsMaturity Time to Yield to

Inputs Date Maturity Maturity

Today 07/07/09

One month Treasury Bill 08/07/09 0.09 3.96%

Three month Treasury Bill 10/04/09 0.24 5.19%Six month Treasury Bill 01/03/10 0.49 5.43%

One year Treasury Bill 07/07/10 1.00 5.78%

Two Year Investment Bond 07/07/11 2.00 5.94%

Three Year Investment Bond 07/06/12 3.00 5.99%

Four Year Investmetn Bond 07/06/13 4.00 6.05%

Five Year Investment Bond 07/06/14 5.00 6.26%

Ten Year Investment Bond 07/06/19 10.00 6.56%

Fifteen Year Investment Bond 07/06/24 15.00 6.59%

Twenty Year Investment Bond 07/07/29 20.00 6.54%

Twenty Five Year Investment Bond 07/05/34 24.99 6.34%

Thrity Year Investment Bond 07/07/39 30.00 6.08%

- 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00

3.75%

4.00%

4.25%

4.50%

4.75%

5.00%

5.25%

5.50%

5.75%

6.00%

6.25%

6.50%

6.75%

U.S. Treasury Zero - Coupon Yield Curv


YieldtoM

aturity(Annual)


17/54


18/54

STOCK VALUATION - Dynamic Chart

Inputs

Inflation Rate 3.00% 6

Earning Retention Rate 50.00% 5

Outputs

Real Discount Rate (Real K) 9.00% 7.00% 8.00% 9.00%

Intrinsic Value / Share $176.26 $318.27 $226.97 $176.26

Nominal Discount Rate (k) 12.27%

Historical Data

Period -2 -1 0 1

Inflation Rate 2.80% 2.80% 3.00%

Reat Return on Investment (Real ROI) 22.30% 20.70% 19.00%

Nominal Return on Investment 25.70% 24.40% 22.57%

Real Growth Rate in Dividend (Real g) 11.20% 10.40% 9.50%

Nominal Growth Rate in Dividend (g) 14.50% 13.70% 12.79%

Nominal Dividend / Share $5.10 $5.84 $6.64 $7.49

Continuation Value / Share

Sum of Future Div. & Con. Value / Shr $7.49

PV of Future Div. & Cont. Value / Shr $6.67

Intrinsic Value/Share $176.26

7.

$100.00

$125.00

$150.00

$175.00

$200.00

$225.00

$250.00

$275.00

$300.00

$325.00

IntrinsicValue/Sh

are


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10.00% 11.00% 12.00%

$144.00 $121.67 $105.30

Stage : 2

Infinite

Stage 1 : Explicit Forecast Horizon

Horizon (ROI > k) (ROI = k)

2 3 4 5 6

3.00% 3.00% 3.00% 3.00% 3.00%

17.00% 15.00% 13.00% 11.00% 9.00%

20.51% 18.45% 16.39% 14.33% 12.27%

8.50% 7.50% 6.50% 5.50% 4.50%

11.76% 10.73% 9.69% 8.66% 7.64%

$8.37 $9.27 $10.17 $11.05 $11.89

$256.51

$8.37 $9.27 $10.17 $267.56

$6.64 $6.55 $6.40 $150.00

0% 8.00% 9.00% 10.00% 11.00% 12.00%

Dynamic Chart of Two Stage Dividend Discount Model

Real Discount Rate


20/54

STOCK VALUATION - TWO STAGE

Inputs

Inflation Rate 3.00%

Real Discount Rate (Real k) 9.00%

Earning Retention Rate 50.00%

Outputs

Nominal Discount Rate (k) 12.27%

Historical Data

Period -2 -1 0 1

Inflation Rate 2.80% 2.80% 3.00%

Reat Return on Investment (Real ROI) 22.30% 20.70% 19.00%

Nominal Return on Investment 25.70% 24.40% 22.57%

Real Growth Rate in Dividend (Real g) 11.20% 10.40% 9.50%

Nominal Growth Rate in Dividend (g) 14.50% 13.70% 12.79% Nominal Dividend / Share $5.10 $5.84 $6.64 $7.49

Continuation Value / Share

Sum of Future Div. & Con. Value / Shr $7.49

PV of Future Div. & Cont. Value / Shr $6.67

Intrinsic Value/Share $176.26


21/54

Stage : 2

Infinite

Stage 1 : Explicit Forecast Horizon

Horizon (ROI > k) (ROI = k)

2 3 4 5 6

3.00% 3.00% 3.00% 3.00% 3.00%

17.00% 15.00% 13.00% 11.00% 9.00%

20.51% 18.45% 16.39% 14.33% 12.27%

8.50% 7.50% 6.50% 5.50% 4.50%

11.76% 10.73% 9.69% 8.66% 7.64%$8.37 $9.27 $10.17 $11.05 $11.89

$256.51

$8.37 $9.27 $10.17 $267.56

$6.64 $6.55 $6.40 $150.00


22/54

BOND VALUATION - System of Five bond Varia

Annual Percentage Rate

Inputs

Rate Convetion (1= EAR, 0=APR) 0 EAR = Effective Annual Rate Convention & APAnnual Coupon Rate (CR) 5.00%

Yield to Maturity (Annualized) (Kd) 9.00%

Number of Payment / Year (NOP) 2.00

Numer of Periods to Maturity (N) 8


Discount Rate / Period (DR) 4.50% =IF($C$6=1,((1+Kd)^(1/NOP))-1,Kd/NOP)


Bond Price (VB) $868.08 =-PV(DR,N,INT,M)

(1) Number of Periods to Maturity (N)

Number of Periods to Maturing using the NPER Function 8 =NPER(DR,IN

(2) Face Value (M)

Face Value using the FV Function $1,000.00 =FV(DR,N,IN

Face Value using the Formula $1,000.00 =VB*((1+DR)

(3) Find Discount Rate / Period (DR)

Discount Rate / Period using the RATE Function 4.50% =RATE(N,INT

(4) Coupon Payment (INT)

Coupon Payment using the PMT Function $25.00 =PMT(DR,N,-

Coupon Payment using the Formula $25.00 =(VB-M/((1+D

(5) Bond Price (VB)Bond Price using the PV Function $868.08 =-PV(DR,N,IN

Bond Price using the Formula $868.08 =INT*(1-((1+


23/54

bles

R = Annual Percentage Rate Convention

T,-VB,M)

,-VB)

N)-INT*(((1+DR)^N)-1)/DR

,-VB,M)

B,M)

R)^N))/((1-((1+DR)^(-N)))/DR)

,M)

R)^(-N)))/DR+M/((1+DR)^N)


24/54

BOND VALUATION - BY YIELD TO MATURI

Effective Annual Rate

Inputs






Output



Chart Outputs

Yield to Maturity (Annualized) 1% 2% 3% 4%

Discount Rate / Period 0.50% 1.00% 1.49% 1.98%

Bond Price $1,232.54 $1,169.44 $1,110.36 $1,055.02

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

$750.00

$800.00

$850.00

$900.00

$950.00

$1,000.00

$1,050.00

$1,100.00

$1,150.00

$1,200.00

$1,250.00

Bond Price


25/54

TY


5% 6% 7% 8% 9% 10% 11%

2.47% 2.96% 3.44% 3.92% 4.40% 4.88% 5.36%

$1,003.13 $954.46 $908.77 $865.85 $825.50 $787.55 $751.83


26/54

BOND VALUATION - BY YIELD TO MATURI


Inputs






Output



Chart Outputs

Yield to Maturity (Annualized) 1% 2% 3% 4%

Discount Rate / Period 0.50% 1.00% 1.50% 2.00%

Bond Price $1,232.38 $1,168.83 $1,109.08 $1,052.88

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

$700.00

$750.00

$800.00

$850.00$900.00

$950.00

$1,000.00

$1,050.00

$1,100.00

$1,150.00

$1,200.00

$1,250.00

Bond Price


27/54

TY


5% 6% 7% 8% 9% 10% 11%

2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50%

$1,000.00 $950.23 $903.37 $859.22 $817.63 $778.42 $741.44


28/54

BOND VALUATION - BASIC


Inputs






Output



Period 0 1 2 3

Time (Years) 0 0.5 1 1.5

Cash Flows $25.00 $25.00 $25.00

Present Value of Cash Flow $23.92 $22.89 $21.91

Bond Price $817.63 =sum(d19:o19)

Calculate Bond Price using the Formula

Bond Price $817.63 =INT*(1-((1+DR)^(-N)))/DR+M/((1+DR)^N)

Calculate Bond Price using the PV Function

Bond Price $817.63 =-PV(DR,N,INT,M)


29/54


4 5 6 7 8 9 10

2 2.5 3 3.5 4 4.5 5

$25.00 $25.00 $25.00 $25.00 $25.00 $25.00 $25.00

$20.96 $20.06 $19.20 $18.37 $17.58 $16.82 $16.10


30/54

11 12

5.5 6

$25.00 $1,025.00

$15.40 $604.41


31/54

LOAN AMORTIZATION - Sensitivity Anal

Inputs

Present Value $300,000.00

Interest Rate / year 8%

Number of Years 30

Output

Year 1 2 3 4

Beginning Principal Balance $300,000.00 $297,351.77 $294,491.68 $291,402.79

Payment $26,648.23 $26,648.23 $26,648.23 $26,648.23

Interest Component $24,000.00 $23,788.14 $23,559.33 $23,312.22

Principal Component $2,648.23 $2,860.09 $3,088.90 $3,336.01

Data Table : Sensitivity of the Interest Component to the Interest Rate / Year

Input Values for

Interest Rate / Year

6.00% $18,000.00 $16,920.00 $16,984.80 $16,980.917.00% $21,000.00 $19,530.00 $19,632.90 $19,625.70

8.00% $24,000.00 $22,080.00 $22,233.60 $22,221.31

9.00% $27,000.00 $24,570.00 $24,788.70 $24,769.02

10.00% $30,000.00 $27,000.00 $27,300.00 $27,270.00

Data Table : Sensitivity of the Principal Component to the Interest Rate / Year

Input Values for

Interest Rate / Year

6.00% $1,260.00 $17,924.40 $16,924.54 $16,984.53

7.00% $1,470.00 $20,897.10 $19,537.20 $19,632.40

8.00% $1,680.00 $23,865.60 $22,090.75 $22,232.74

9.00% $1,890.00 $26,829.90 $24,585.31 $24,787.32

10.00% $2,100.00 $29,790.00 $27,021.00 $27,297.90


32/54

sis

5 6 7 8 9 10 11

$288,066.78 $284,463.89 $280,572.77 $276,370.36 $271,831.76 $266,930.07 $261,636.25

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$23,045.34 $22,757.11 $22,445.82 $22,109.63 $21,746.54 $21,354.41 $20,930.90

$3,602.89 $3,891.12 $4,202.41 $4,538.60 $4,901.69 $5,293.82 $5,717.33

$16,981.15 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13$19,626.20 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,222.30 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,770.79 $24,770.63 $24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,273.00 $27,272.70 $27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73

$16,980.93 $16,981.14 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13

$19,625.73 $19,626.20 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,221.38 $22,222.29 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,769.14 $24,770.78 $24,770.63 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,270.21 $27,272.98 $27,272.70 $27,272.73 $27,272.73 $27,272.73 $27,272.73


33/54

12 13 14 15 16 17 18

$255,918.92 $249,744.20 $243,075.51 $235,873.32 $228,094.96 $219,694.32 $210,621.64

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$20,473.51 $19,979.54 $19,446.04 $18,869.87 $18,247.60 $17,575.55 $16,849.73

$6,174.72 $6,668.69 $7,202.19 $7,778.36 $8,400.63 $9,072.68 $9,798.50

$16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13$19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73

$16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13

$19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73


34/54


35/54

26 27 28 29 30

$106,398.66 $88,262.32 $68,675.07 $47,520.85 $24,674.29

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$8,511.89 $7,060.99 $5,494.01 $3,801.67 $1,973.94

$18,136.34 $19,587.24 $21,154.22 $22,846.56 $24,674.29

$16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13$19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73

$16,981.13 $16,981.13 $16,981.13 $16,981.13 $16,981.13

$19,626.17 $19,626.17 $19,626.17 $19,626.17 $19,626.17

$22,222.22 $22,222.22 $22,222.22 $22,222.22 $22,222.22

$24,770.64 $24,770.64 $24,770.64 $24,770.64 $24,770.64

$27,272.73 $27,272.73 $27,272.73 $27,272.73 $27,272.73


36/54

LOAN AMORTIZATION - BASIC

Inputs

Present Value $300,000.00

Interest Rate / year 8.00%

Number of Years 30

Output

Year 1 2 3 4

Beginning Principal Balance $300,000.00 $297,351.77 $294,491.68 $291,402.79

Payment $26,648.23 $26,648.23 $26,648.23 $26,648.23

Interest Component $24,000.00 $23,788.14 $23,559.33 $23,312.22

Principal Component $2,648.23 $2,860.09 $3,088.90 $3,336.01

Column

Column

Column

Column

Column

Column

Column I

Column J

Column

Column

Column

Column

Column

Column

Column

Cl

Column

Column

Clm

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Column CColumn DColumn EColumn FColumn GColumn HColumn IColumn JColumn KColumn LColumn MColumn NColumn OColumn PColumn QColu

Column CColumn DColumn EColumn FColumn GColumn HColumn IColumn JColumn KColumn LColumn MColumn NColumn OColumn PColumn QColu

Loan Amortizati

Year

%


37/54

5 6 7 8 9 10 11

$288,066.78 $284,463.89 $280,572.77 $276,370.36 $271,831.76 $266,930.07 $261,636.25

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$23,045.34 $22,757.11 $22,445.82 $22,109.63 $21,746.54 $21,354.41 $20,930.90

$3,602.89 $3,891.12 $4,202.41 $4,538.60 $4,901.69 $5,293.82 $5,717.33

Column

o

n

Column

Column

Column

Column

Column

Column

Column

Column

Column

Column

Column

Column

Column

Column

mn RColumn S

Column TColumn U

Column VColumn W

Column XColumn Y

Column ZColumn AA

Column ABColumn AC

Column AD

Column AE

Column

mn RColumn SColumn TColumn UColumn VColumn WColumn XColumn YColumn ZColumn AAColumn ABColumn ACColumn ADColumn AEColumn

on - Basic


38/54

12 13 14 15 16 17 18

$255,918.92 $249,744.20 $243,075.51 $235,873.32 $228,094.96 $219,694.32 $210,621.64

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$20,473.51 $19,979.54 $19,446.04 $18,869.87 $18,247.60 $17,575.55 $16,849.73

$6,174.72 $6,668.69 $7,202.19 $7,778.36 $8,400.63 $9,072.68 $9,798.50


39/54

19 20 21 22 23 24 25

$200,823.14 $190,240.76 $178,811.79 $166,468.51 $153,137.76 $138,740.55 $123,191.56

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$16,065.85 $15,219.26 $14,304.94 $13,317.48 $12,251.02 $11,099.24 $9,855.32

$10,582.38 $11,428.97 $12,343.29 $13,330.75 $14,397.21 $15,548.99 $16,792.91


40/54

26 27 28 29 30

$106,398.66 $88,262.32 $68,675.07 $47,520.85 $24,674.29

$26,648.23 $26,648.23 $26,648.23 $26,648.23 $26,648.23

$8,511.89 $7,060.99 $5,494.01 $3,801.67 $1,973.94

$18,136.34 $19,587.24 $21,154.22 $22,846.56 $24,674.29


41/54

REAL AND INFLATION - GENERAL DISCOUNT RATE(In Thousands of $)

Inputs

Preiod 0 1 2 3 4

Current Investments 100

Future Value of each Cash Flow 21.00 34.00 40.00 33.00

Inflation Rate 3.00% 2.80% 2.50% 2.20%

Real Discount Rate 5.00% 5.50% 6.00% 6.50%

Net Present Value using a Time Line

Preiod 0 1 2 3 4

Discount Rate 8.15% 8.45% 8.65% 8.84%

Cumulative Discount Factor 0.00% 8.15% 17.29% 27.44% 38.71%

Cash Flows $(100.00) $21.00 $34.00 $40.00 $33.00

Present Value of each Cash Flow $(100.00) $19.42 $28.91 $31.19 $23.51

Net Present Value $14.26


42/54

5

17.00

2.00%

6.50%

5

8.63%

50.68%

$17.00

$11.24


43/54

REAL AND INFLATION - CONSTANT DISCOUNT RATE(In Thousands of $)

Inputs

Inflation Rate 3.00%

Real Discount Rate 5.00%

Preiod 0 1 2 3 4



Outputs

Discount Rate 8.15%


Preiod 0 1 2 3 4

Cash Flows $(100.00) $21.00 $34.00 $40.00 $33.00


Net Present Value 15.72

Net Present Value Using the NPV Function 15.72


44/54

5

17.00

5

$17.00

$11.49


45/54

NET PRESENT VALUE - GENERAL DISCOUNT RATE(In Thousands of $)

Inputs

Preiod 0 1 2 3 4



Discount Rate 8.00% 7.60% 7.30% 7.00%


Preiod 0 1 2 3 4

Cumulative Discount Factory 0 8.00% 16.21% 24.69% 33.42%

Cash Flows $(100.00) $21.00 $34.00 $40.00 $33.00




46/54

5

17.00

7.00%

5

42.76%

$17.00

$11.91


47/54

NET PRESENT VALUE - CONSTANT DISCOUNT RATE(In Thousands of $)

Inputs

Discount Rate 8%

Preiod 0 1 2 3 4




Preiod 0 1 2 3 4

Cash Flows -100 21.00 34.00 40.00 33.00

Present Value of each Cash Flow -100.00 19.44 29.15 31.75 24.26


Net Present Value using the NPV Function



48/54

5

17.00

5

17.00

11.57


49/54

ANNUITY - SYSTEM OF FOUR ANNUITY VARIABLES

Inputs

Payments 80

Discount Rate / Period 6%

Number of Periods 5

Present Value 336.99

Payments

Payments using the Formula 80

Payments using the PMT Function 80

Discount Rate/Period

Discount Rate/ Per Usion the RATE Function 6.00%

Number of Periods

Num of Periods using NPER Function 5

Present Value using a Time LinePreiod 0 1 2 3 4

Cash Flows 0 80 80 80 80

Present Value of each Cash Flow 0.00 75.47 71.20 67.17 63.37


Present Value using the formula


Present Value using the FV Function



50/54

5

80

59.78


51/54

ANNUITY - FUTURE VALUE

Inputs

Payments 80


Number of Periods 5

Future Value using a Time Line

Preiod 0 1 2 3 4 5

Cash Flows 0 80 80 80 80 80

Future Value of each Cash Flow 0.00 101.00 95.28 89.89 84.80 80.00

Future Value 450.97

Future Value using the formula

Future Value 450.97

Future Value using the FV Function

Future Value 450.97


52/54

ANNUITY - PRESENT VALUE

Inputs

Payments 80


Number of Periods 5

Present Value using a Time Line

Preiod 0 1 2 3 4 5

Cash Flows 0 80 80 80 80 80

Present Value of each Cash Flow 0.00 75.47 71.20 67.17 63.37 59.78




Present Value using the PV Function



53/54

SINGLE CASH FLOW - FUTURE VALUE

Inputs

Single Cash Flow 747.26


Number of Periods 5

Future Value using a Time Line

Preiod 0 1 2 3 4 5

Cash Flows 747.26 0 0 0 0 0

Future Value of each Cash Flow 1000.00 0.00 0.00 0.00 0.00 0.00

Future Value 1000.00

Future Value using the formula


Future Value using the PV Function



54/54

SINGLE CASH FLOW - PRESENT VALUE

Inputs

Single Cash Flow 1000


Number of Periods 5

Present Value using a Time Line

Preiod 0 1 2 3 4 5

Cash Flows 0 0 0 0 0 1000

Present Value of each Cash Flow 0.00 0.00 0.00 0.00 0.00 747.26




Present Value using the PV Function


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