Question 8.P.12: The ABC Company is considering the purchase of a new sanding......
The ABC Company is considering the purchase of a new sanding machine; machine models A and B are available. Both models have a five-year life, and their cash flows are as given in Table 8-2. The interest rate is 10% per year, compounded annually. Which model should ABC buy?
| Table 8-2 | ||
| End of year | Cash Flows | |
| Model A | Model 2 | |
| 0 | -$30 000 | -$30 000 |
| 1 | 10 000 | 30 000 |
| 2 | 10 000 | 5 000 |
| 3 | 10 000 | 3 000 |
| 4 | 10 000 | 2 000 |
By the net present value method:
NPV_A = -$30 000 + $10 000(P/A, 10%, 4) = -$30 000 + $10 000(0.31547)^{-1} = $1698.74
NPV_B = -$30 000 + $30 000(P/F, 10%, 1) + $5000(P/F, 10%, 2) + $3000(P/F, 10%, 3)
+ $2000(P/F, 10%, 4) = $5024.93
By the payback period method:
PBP_A = \frac{\$30 000}{\$10 000 \text{per year}} = 3 \text{years} \quad PBP_B = 1 \text{year}By the rate of return method:
for model A 0 = -$30 000 + $10 000(P/A, i *%, 4)
(A/P, i *% ,4) = 0.33333
and by linear interpolation in Appendix A,
i* ≈ 12% + \frac{0.33333 – 0.32923}{0.35027 – 0.33333}(15% – 12%) = 12.24%
for model B 0 = -$30 000 + $30 000(P/F, i*%, 1)
+ $5000(P/F, i*%, 2) + $3000(P/F, i*%, 3) + $2000(P/F, i*%, 4)
By trial and error:
\begin{array}{c | c} i^* & NPV \\ \hline 20\% & \$1172.84 \\ 25\% & -\$435.48 \end{array}and by linear interpolation,
i* ≈ 20% + \frac{\$0 – \$1172.84}{-\$435.48 – \$1172.84}(25% – 20%) = 23.65%
It is seen that all three methods rate model B above model A; ABC should purchase model B.