Consider the following information on Wellington Power Co. Debt: 4,000, 7% semia

Question

Consider the following information on Wellington Power Co.

Debt: 4,000, 7% semiannual coupon bonds outstanding, $1,000 par value, 18 years to maturity, selling for 102 percent of par; the bonds make semiannual payments.

Preferred Stock:  10,000 outstanding with par value of $100 and a market value of 105 and $10 annual dividend.

Common Stock: 84,000 shares outstanding, selling for $56 per share, the beta is 2.08

The market risk premium is 5.5%, the risk free rate is 3.5% and Wellington's tax rate is 32%.

Wellington Power Co. is evaluating two mutually exclusive project that is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and decided to apply an adjustment factor of +2.1% to the cost of capital for both projects.

Project A is a five-year project that requires an initial fixed asset investment of $2.4 million. The fixed asset falls into the five-year MACRS class. The project is estimated to generate $2,050,000 in annual sales, with costs of $950,000. The project requires an initial investment in net working capital of $285,000 and the fixed asset will have a market value of $225,000 at the end of five years when the project is terminated.

Project B requires an initial fixed asset investment of $1.0 million. The marketing department predicts that sales related to the project will be $920,000 per year for the next five years, after which the market will cease to exist. The machine will be depreciated down to zero over four-year using the straight-line method (depreciable life 4 years while economic life 5 years). Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales.  The project will also require an addition to net working capital of $150,000 immediately. The asset is expected to have a market value of $120,000 at the end of five years when the project is terminated.

Use the following rates for 5-year MACRS: 20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%

1)     What is the appropriate discount rate for project A and project B?

2)     Calculate project A's cash flows for years 0-5

3)     Calculate project B's cash flows for year 0-5

Explanation / Answer

Both net present value and internal rate of return are methods used to determine the value of a business, project, or financial asset with a limited expected life span.

Net present value is used to determine how much you should be willing to pay for the investment given a certain discount rate.

Internal Rate of Return is found when you know how much you plan to spend, know the future cash flows, and want to find the discount rate implied by the project. The Internal Rate of Return (or IRR) is used to tell you what annual rate of return the project will earn you given that the project will one day end with a final positive cash flow or negative cash flow.

For example if I wanted to invest in an airplane and expected the airplane to cost $10 million and generate $2 million dollars per year, that would imply a 20% annual return. However that assumes that the airplane would last forever, and the cash flows would keep on coming in. In reality though the airplane will one day become worn out and will have to be scrapped. Let's pretend this takes 10 years.

So then realizing that the plane will be worthless after 10 years, what is the internal rate of return? It is going to be much lower than 20%, it will be the discount rate where the net present value of the airplane is zero.

So let's try to find the zero point using net present value (guess and check method).

Assuming we can earn 10% someplace else (the discount rate) what is the net present value of the plane?

NPV = PV of cash flow yr 0 + PV of yr 1 cash flow + PV of yr 2 cash flow + PV of yr 3 cash flow, etc until yr 10.

PV of year 0 is -$10 million (for the cost of the plane).

NPV = -10 + ......

At the end of year one we will have earned $2 million in profits, but since we won't earn that for 1 full year we need to discount the $2 million back to present value at the discount rate of 10%.

$2 million / 1.1 = 1.81

NPV = -10 + 1.81 + .............

At the end of year 2 we will have earned another $2 million in profit but won't earn it for 2 years:

$2 million / 1.1^2 = 1.65289

NPV = -10 + 1.81 + 1.653 .......

***I'll use a financial calculator to determine the rest:

NPV = $2,289,134.21

So that is the present value of the profit we will receive after 10 years owning the plane. In actuality we will have earned $20 million in total profits, will have paid $10 million for a the plane, so will have netted out $10 million in profits, but it will only feel like $2.29 million because those cash flows will be spread out over 10 years and we could have been earning 10% interest during those 10 years.

The good news is that the cash flow is positive, so we are better off investing in the plane then we are investing in something that only earns 10%. But what if we could earn 11% elsewhere, or 12%?

The IRR calculates what rate of return we would get from the project given that the plane will one day be retired so we know what rate we would have to be able to earn elsewhere in order to decide not to buy the plane.

We could keep calculating NPV and trying different discount rates until NPV was equal to zero to find IRR. Or we could use a financial calculator. According to my financial calculator

IRR = 15.10%

So we are buying a plane for $10 million dollars and will receive annual cash flows of $2 million per year. If the plane lasted forever we would have ourselves a 20% return! But it will have to be scrapped after 10 years at which point our initial investment will be gone. So including that, the actual internal rate of return of the project is only 15.1%.

And if you calculate the NPV of the plane assuming a 15.1% discount rate you should end up with NPV = $0.

That should help explain the difference between NPV and IRR.

3 years ago

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.