equivalence of cash flows construction engineering 221

Equivalence of cash flows

Construction Engineering 221


• Non- annual compounding (discounting)– A sum of money invested at 4% annual

interest is compounded semi-annually. How many years will it take for the invested sum to double in value:

• i = 2%, F = 2P, n = ?• Go to the 2% tables (page 100)• Find n where F/P = 2 (n= 35)• 35 semiannual periods equal 17.5 years


• If a 5 year balloon lease has a 10% annual rate, but interest is charged monthly (like a credit card), what will be the buyout amount on a $2500 purchase?– F = 2500(1 + .10/12)60 or

• 2500(1.6453) = 4113.25

•


• What if the lease caps are compounded annually:– F = 2500 (n=5, i=.10) or1.6105– Buyout is 4026.25– Lender makes an additional $87 merely by

compounding the interest monthly instead of annually


Cash flow factors and symbols

take the formula and solve using table factors. Expressed as:

F = P(F/P, i, n) or

P = F(P/F, i, n)

Other equivalencies use the same procedure


• Uniform series equivalence– Repeating cash flow for a known number of

periods is called and annual amount (like a mortgage payment). Can be estimated (like maintenance) or known (like rental income)

– Future worth of a annual payment (called an annuity) is F = A(F/A, i, n) where A is the size of the annual amount


• Sinking fund is an account that you must make deposits in each year in order to have F dollars at n periods in the future. Therefore, the A/F factor is called the sinking fund factor, and A is the sinking fund allocation


• An annuity is a series of equal payments made over a period of time (for instance, a bond that pays interest annually). Therefore, the P/A factor is called the annuity factor and A is the annuity amount

• When the stream of payments is “perpetual” (like a building generating rents), the term capitalized cost is sometimes used.

• Capitalized cost is P = A/i


• Assume you have a client who wants to net lease the project on a 25 year lease. They can afford $20,000 a month in lease payments ($240,000 per year using end of year convention)

• What should the capital budget be for the new building if you are the turnkey contractor and your cap rate is 8%?

• P = 240,000(10.6748 {p. 124}), or $2,562,000


• If the building could be re-leased for another 25 years at the same rate, the initial cost budget would be:– 240,000 (12.2335) = 2,936,000– An infinite series of 240,000 annual payments

has a present worth of 240,000/.08 or 3,000,000, so you can see that for many buildings, the capitalized cost formula is a viable option


• Can calculate “past worth” by setting t=o at some arbitrary point in the cash flow series. Sometimes this calculation is needed in lawsuits to award damages or determine remedies for loss of use

• Can also calculate periods needed to earn a multiple of investment. Table 2 on Page 16 give double and triple earnings. – n= log X/ log (1 + i), where X is the multiple desired

on the initial investment


• Variable (non-standard flows)– Gradient cash flows are better

representations of many equipment maintenance schedules than uniform series (gets more expensive to maintain as the equipment gets older)

– The gradient starts in year 2 because it is the INCREASE in annualized payments that are of interest


• P/G factor calculates the present worth of the ESCALATING costs, not the base costs

• Base costs must be calculated using the P/A factor

• Maintenance costs are the most typical example of gradient series


• Stepped cash flows are handled as two separate cash flows using the superpositioning technique (see example on page 19). This would apply to a rental contract with an escalation clause

• Missing or extra cash flows can be handled similarly (major overhaul example), as can beginning of period payments

equivalence of cash flows construction engineering 221

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