Question

1. Smith Corporation has a cost capital of 10% and is currently considering an investment of $825 m. This investment is expected to generate after-tax cash flows of $253 m per year for 7 years and an additional after-tax salvage of $110 m in year 7. What is the investment's profitability index?

A. 1.19

B. 1.33

C. 1.56

2. Which of the following statements is least likely to be correct?

A. The NPV profile graphed the NPV of a capital project at different discount rates.

B. Decisions for mutually exclusive, conventional projects will be consistent when using the NPV and IRR approaches.

C. The NPV approach uses a more realistic discount rate and should be used to assess mutually exclusive projects.

Answer 1

1.

Profitability index = Present value of future cash flows/Initial investment

Present value of future cash flows = Annual cash flow x PVIFA (i, n) + Salvage value x PVIF (i, n)

                       = $ 253 m x PVIFA (10 %, 7) + $ 110 m PVIF (10 %, 7)

                       = $ 253 m x [1 – (1+0.1)^-7/0.1] + $ 110 m x (1+0.1)^-7

                       = $ 253 m x [1 – (1.1)^-7/0.1] + $ 110 m x (1.1)^-7

                   = $ 253 m x [(1 –0.513158118230706)/0.1] + $ 110 m x 0.513158118230706

                       = $ 253 m x (0.486841881769294/0.1) + $ 56.4473930053777 m

                   = $ 253 m x 4.86841881769293 + $ 56.4473930053777 m

                       = $ 1,231.70996087631 m + $ 56.4473930053777 m

                     = $ 1,288.15735388169 m

Profitability index = $ 1,288.15735388169 m/$ 825 m

                              = 1.56140285318993 or 1.56

Hence option “C. 1.56” is correct answer.

2.

When comparing two mutually exclusive projects, the NPV and IRR rules may provide conflicting results.

One project may have higher NPV while other may have higher IRR due to the different cash flow patterns for the two projects.

Hence statement B is least likely to be correct.

Option “B. Decisions for mutually exclusive, conventional projects will be consistent when using the NPV and IRR approaches.” is correct answer.