Question

HW15-11)

Middlefield Motors is evaluating project Z. The project would require an initial investment of 76,000 dollars that would be depreciated to 11,000 dollars over 8 years using straight-line depreciation. The first annual operating cash flow of 27,500 dollars is expected in 1 year, and annual operating cash flows of 27,500 dollars are expected each year forever. Middlefield Motors expects the project to have an after-tax terminal value of 388,000 dollars in 4 years. The tax rate is 15 percent. What is (X+Y)/Z if X is the project’s relevant expected cash flow for NPV analysis in year 4, Y is the project’s relevant expected cash flow for NPV analysis in year 5, and Z is the project’s relevant expected cash flow for NPV analysis in year 3? Round your answer to 2 decimal places (for example, 2.89, 0.70, or 1.00).

Answer 1

In the above question the relevant cash flow for NPV analysis is the present value of th ecash flows of a specific year i.e. dicounting a particular future year cash flow to today.

For this we would require the discounting factor or cost of capital being considered. We know the terminal cash flow i.e. 388,000 in year four which is given by the relationship CF *(1+G)/Kc where G is growth rate in cash flows and Kc is the cost of capital.

Here CF is the yearly cash flow based on the given figures Operating Cash flow - (Cashflow-depreciation) * tax rate

= $27,500 - [(27,500-8,125)*15%] = 27,500 - 2906.25 = 24,594

Now terminal value of 388,000 = 24,594 &(1+G) / Kc; G is 0 as the question says cash flows are constant throughout so 388,000 = 24,544/Kc so Kc = 24,594/388,000 = 6.34%

so X (Pv of year 4) = 24,594 / (1.0634^4) = 19,233

so Y (Pv of year 5) = 24,594 / (1.0634^5) = 18,086

so Z (Pv of year 3) = 24,594 / (1.0634^3) = 20,452

(X+Y)/Z = (18,086+19,233)/20452 = 1.82