Example 2.5

Decisions Involving the Time Value of Money

Background Information

Acron is a large drug company. One of its new drugs, Niagara, is coming to market and Acron needs to determine how much annual production capacity to build for this drug.

Government regulations make it difficult to add capacity at a later date, so Acron must determine a capacity recommendation before the drug comes to market.

The drug will be sold for 20 years before it comes off patent. After the 20 years, the rights to produce the drug are virtually worthless.

Background Information -- continued Acron has made the following assumptions:

– Year 1 demand will be 10,000 units

– During years 2-6, annual growth of demand will be 15%.

– During years 7-20, annual growth of demand will be 5%.

– It costs $6, payable at the end of year 1, to build each unit of annual production capacity. The cost of the building capacity is deprecisted on a straight-line 5-year basis.

– During year 1, Niagara will sell for $8 per unit and will incur a variable cost $5 to produce.

Background Information -- continued

– The cost of maintaining a unit capacity during year 1 is $1.

– The sales price, unit variable cost, and unit capacity maintenance cost will increase by 5% per year.

– Profits are taxed at 40%.

– All cash flows are assumed to occur at the end of each year, and the corporate discount rate is 10%

Background Information -- continued Acron wants to develop a spreadsheet model of its

20-year cash flows. Then it wants to answer the following questions.

– What capacity level should be chosen?

– How does a change in the discount rate affect the optimal capacity level?

– How realistic is the model?

The Model The model of Acron’s cash flows appears on the next

slide.

As with many financial spreadsheet models that extend over a multi-year period, this model is not as bad as it looks.

Usually, we enter “typical” formulas in the first year or two and then copy this logic across to all years.

The Model -- continued To create the model, enter the given data in the input

section, enter any trial value for the capacity decision in the Capacity cell, name ranges, and complete the following steps.

– Building cost and depreciation. Enter the toal building cost in the BuildingCost cell with the formula =Capacity*UnitCapCost then enter the depreciation over the first 5 years by entering the formula =BuildingCost*DepredRate in cell B24 and copying it across to cell F24.

The Model -- continued– Demand and units sold. The demand is governed by the

percentage rate increases assumed by Acron. However, the number of units that can be sold is limited to building capacity. Therefore we enter the formula =Demand1 in cell B26 and the formula =B26*(1+DemGrowth2_6) in cell C26 and copy it across to cell G26, enter the formula =G26*(1+DemGrowth7_20) in cell H26 and copy it across to U26. Then enter the formula =MIN(B26,Capacity) in cell B27 and copy it across to cell U27.

– Unit prices and costs. The unit selling price and unit costs all grow by the same inflation factor. To calculate them for year 1, enter the formulas =UnitPirice1, =UnitVCost1, and =UnitMaintCost1 in cells B29, B30 and B31. Then for all other years, enter the formula =B29*(1+InflRate) in cell C29 and copy it to the range C29:U31.

The Model -- continued

– Revenues and costs. The revenues and variable costs depend on the number of units sold, so enter the formula =B$27*B29 in cell B33 and copy it to the range B33:U34. Then to calculate the maintenance cost, enter the formula =Capacity*B31 in cell B35 and copy it across to cell U35.

– Pretax profits, after tax profits, and free cash flows. This part is a bit tricky, especially if you are not an accountant. For tax purposes, depreciation is deducted from the difference between revenue and (nonbuilding) costs. Therefore, to obtain pretax profit, the amount on which taxes are based, enter the formula =B33-B34-B35-B24 in cell B37 and copy it across.

The Model -- continued

– Next, subtract taxes to obtain after-tax profits, but keep in mind that there is no tax if there is a loss. This implies the formula =IF(B37<0,B37,B37*(1-TaxRate)) in cell B38, which can be copied across. Finally the free cash flow, the “real” profit after taxes, is found by adding back the depreciation but subtracting the building cost in year 1. To obtain this enter the formula =B38+B24-B23 in cell B39 and copy it across.

– Net present value. The NPV is based on the sequence of cash flows in row 39. From our general discussion of NPV, the value in cell B39 should be multiplied by 1/(1+r)1, the value in cell C39 should be multiplied by 1/(1+r)2, and so on, and these quantities should be summed to obtain the NPV.

The Model -- continued

– Fortunately Excel has a built in NPV function to accomplish this calcualtion. To use it enter the formula =NPV(DiscRate,FreeCashFlow) in the NPV cell This NPV function takes two arguments: the discount rate and a range of cash flows.

Answering the Questions

We now turn to Acron’s first question: How much capacity should it build?

As usual, it is useful to create the data table and corresponding chart shown on the next slide.

These show how NPV varies for different levels of capacity. More specifically, it indicates that Acron can maximize its NPV by using a capacity level of 21,000 units.

Answering the Questions -- continued Question 2 asks about the effect of the discount rate

on optimal capacity.

This is an important question for two reasons.

– First, it is often difficult for a company to determine the appropriate discount rate.

– Second, the NPV is typically quite sensitive to the discount rate.

To answer the questions, we build the two-way data table and corresponding chart. The table and chart follow on the next slides

Optimal Capacity Level Versus Discount Rate

Answering the Questions -- continued For each discount rate, we locate the maximum NPV

and corresponding capacity level and record them in rows 85 and 86.

The chart is based on the values in row 86.

As we see, larger discount rates typically result in lower NPVs because future cash flows are discounted more heavily.

Beyond this, the chart shows how the optimal decreases as the discount rate increases.

Answering the Questions -- continued The reasoning is basically that “bad” things,

especially building costs, tend to occur early, whereas “good” things tend to occur later on.

A higher discount rate magnifies the bad things relative to the good things, so it induces the company to build less capacity.

Finally, we discuss the realism of our model.

Answering the Questions -- continued Probably the major flaw is that we have ignored

uncertainty. It is clear demand, future prices and future costs are highly uncertain.

Of course, there are almost always ways to make any model more realistic – at the cost of increased complexity.

For example, we could model the impact of competition on Niagara’s profitability. We could also realize that Acron’s pricing policy is not set in stone and the price it charges will influence the likelihood that competition will enter the market.

Answering the Questions -- continued Finally, Acron could probably add capacity in the

future if it is experiencing larger than expected demand.

However, it is important to realize that future flexibility in decision making has an impact on the correct decision for today.