Question 14.4: The Waygate Corporation is interested in evaluating a major ...
The Waygate Corporation is interested in evaluating a major new video display technology (VDT). Two competing computer companies have approached Waygate with proposals to develop the technology. Waygate believes that both companies will be able to deliver equivalent products at the end of a five-year period. From the yearly development costs of the VDT for each firm, determine which Waygate should choose if the corporate MARR (investment market rate) is 25\% and price inflation is assumed to be 3.5\% per annum over the next five years. Company Alpha costs: Development costs will be \$150,000 the first year and will increase at a rate of 5\% over the five-year period. Company Beta costs: Development costs will be a constant \$150,000 per year in terms of today’s dollars over the five-year period.
The costs for each of the two alternatives are as follows:
| Year | Actual_Dollar Costs
Stated by Alpha |
Real_Dollar Costs
Stated by Beta |
| 1 | \$150,000×(1.05)^{0}=\$150,000 | \$150,000 |
| 2 | 150,000×(1.05)^{1}=157,500 | 150,000 |
| 3 | 150,000×(1.05)^{2}=165,375 | 150,000 |
| 4 | 150,000×(1.05)^{3}=173,644 | 150,000 |
| 5 | 150,000×(1.05)^{4}=182,326 | 150,000 |
We inflate (or escalate) the stated yearly cost given by Company Alpha by 5% per year to obtain the actual dollars each year. Company Beta’s costs are given in terms of today-based real dollars.
Using a Real-Dollar Analysis
Here we must convert the actual costs given by Company Alpha to real today-based dollars. We do this by stripping the right number of years of general inflation from each year’s cost using (P/F,f, n) or
(1 + f)^{-n} .
| Year | Actual_Dollar Costs
Stated by Alpha |
Actual_Dollar Costs
Stated by Alpha |
| 1 | \$150,000×(1.35)^{-1}=\$144,928 | \$150,000 |
| 2 | 157,500×(1.35)^{-2}=147,028 | 150,000 |
| 3 | 165,375×(1.35)^{-3}=149,159 | 150,000 |
| 4 | 173, 644×(1.35)^{-4}=151,321 | 150,000 |
| 5 | 182, 326×(1.35)^{-5}=153,514 | 150,000 |
We use the real interest rate (i′) calculated from Equation 14-1 to calculate the present worth of costs
for each alternative:
1 + i = (1 + i′)(1+ f) or i = i′ + f+ i′ f (14-1)
i′ = (i -f )/(1 + f) = (0.25 – 0.035)/(1 + 0.035) = 0.208
PW of cost (Alpha) = $144,928(P/F, 20.8%, 1) + $147,028(P/F, 20.8%, 2)
+ $149,159(P/F, 20.8%, 3) + $151,321(P/F, 20.8%, 4)
+ $153,514(P/F, 20.8%, 5) = $436,000
PW of cost(Beta) = $150,000(P/A, 20.8%, 5) = $150,000(2.9387) = $441,000
Using an Actual-Dollar Analysis
Here we must convert the real-dollar costs of Company Beta to actual dollars. We do this by using
(F/P,f, n) or (1 + f ) ^{n} to “add in” the correct number of years of general inflation to each year’s cost.
| Year | Actual Costs Stated by alpha | Actual Costs Stated by Beta |
| 1 | \$150,000×(1.05)^{0}=\$150,000 | \$150,000×(1.035)^{1}=\$155,250 |
| 2 | 150,000×(1.05)^{1}=157,500 | 150,000×(1.035)^{2}=160,684 |
| 3 | 150,000×(1.05)^{2}=165,375 | 150,000×(1.035)^{3}=166, 308 |
| 4 | 150,000×(1.05)^{3}=173,644 | 150,000×(1.035)^{4}=172,128 |
| 5 | 150,000×(1.05)^{4}=182, 326 | 150,000×(1.035)^{5}=178,153
|
Using the market interest rate (i), calculate the present worth of costs for each alternative.
PW of cost (Alpha) = $150,000(P/F, 25%, 1) + $157,500(P/F, 25%, 2)
+ $165,375(P/F, 25%, 3) + $173,644(P/F, 25%, 4)
+ $182,326(P/F, 25%, 5) = $436,000
PW of cost(Beta) = $155,250(P/F, 25%, 1) + $160,684(P/F, 25%, 2)
+ $166,308(P/F, 25%, 3) + $172,128(P/F, 25%, 4)
+ $178,153(P/F, 25%, 5) = $441,000
Whether Waygate uses real-dollar or actual-dollar analysis, it should choose Company Alpha’s offer, which has the lower present worth of costs. There may, of course, be intangible elements in the decision that are more important than the 1 \% difference in the costs.