Corporate Finance, Module 5, “Investment Decisions and Net Present Value”

Homework

(The attached PDF file has better formatting.)

A firm invests $10,000 in a project at the end of year 0. It expects to receive nominal cash flows of $2,500 at the end of year 1, $3,500 at the end of year 2, and $7,000 at the end of year 3. Inflation is projected at 9% per year and the real interest rate is 6%.

A.    What is the nominal discount rate? { 1 + R = (1 + inflation) × (1 + real interest rate) }
B.    What is the project’s net present value? (Use the NPV rule.)

Question: Is it common for the discount rate to be in real dollars and the cash flows to be in nominal dollars?

Answer: The discount rate is the firm’s capitalization rate, which is the risk-free rate plus its beta times the market risk premium. The risk-free rate moves in tandem with the inflation rate. If inflation increases 1%, the risk-free rate increases about 1%. The cash flows are estimated by sales personnel, who use nominal dollars.

Question: How does the final exam test this subject?

Answer: The final exam gives scenarios with nominal or real discount rates, nominal or real cash flows, and perhaps infinite time horizons.

Convert the discount rate and the cash flows into the same terms. Use either nominal or real terms, but be consistent for all items.

I understand that for Part A the nominal discount rate is 15.54%. For Part B, is the real discount rate 1.1554/1.09 - 1 = 6%? And then do we discount by this rate? I tried to follow Exercise 5.3 but I didn't quite get it.

[NEAS: The cash flows are in nominal dollars, so we use the nominal dollar discount rate.]

Dear Supreme Being -- With all the respect I could muster for a human supreme being, I do believe that the discount factors should use the nominal interest rate.  [NEAS: yes]

I agree, the title is a bit much.

But what makes you say that? I was just trying to follow the example, and it seemed like there they were using the real interest rate.

They were, but they were also using real cash flows. Wanna see if the results come out the same, using real cash flow with the real discount rate -- compared with using nominal cash flow with the nominal discount rate?  [NEAS: yes]

Do we discount the 10,000 by 1.1554 since its at the end of year 1 or does it not matter for the NPV as of that time?

[NEAS: Use the net present value at the end of year 0.  You do not need to discount to the beginning of year 0.]

I got a negative present value.  Is that what everyone else is getting?

[NEAS: The net present value can be positive or negative.  A negative net present value is not unusual.  The expected net present value is zero in competitive markets, so many projects have negative net present values.

Yeah, I got a negative NPV too: -676.04

Re:

Rachel: The discount rate is the firm’s capitalization rate, which is the risk-free rate plus its beta times the market risk premium. The risk-free rate moves in tandem with the inflation rate. If inflation increases 1%, the risk-free rate increases about 1%. The cash flows are estimated by sales personnel, who use nominal dollars.

It should be the project's beta, not the firm's beta, correct? Otherwise good projects for low-beta firms would be to purchase the stock of high-beta firms...

[NEAS: Yes: if a firm has projects of different risk, use the capitalization rate for the project, not for the entire firm.]