What is the NPV of the project?

Question

Hall Corp. has 25,000 shares of common stock outstanding with a market price of $32 a share and an expected dividend yield of 5.7 percent. Dividends increase by 4.2 percent annually. The firm also has $450,000 of debt outstanding that is selling at 102 percent of par that has a yield to maturity of 6.8 percent. The tax rate is 35 percent. The firm is considering a project that has the same risk level as the firm's current operations, an initial cost of $328,000 and cash inflows of $52,500, $155,000, and $225,000 for Years 1 to 3, respectively. What is the NPV of the project? 

Answer 1

To get the NPV of the project we need to find Hall Corp's discount rate.

The discount rate for Hall Corp is its weighted average cost capital (WACC).

Hulls total capital is the market value of 25,000 shares and market value of the $450,000 par value of debt.

Market Value of Shares is 25,000 * $32 = $800,000

Market Value of Debt is 1.02 * $450,000 = $459,000

Cost of Equity (the stock), call it K, is :

K= Next Dividend/ Stock Price + growth in the dividend

Note: Next Dividend/ Stock Price is the Dividend Rate, which is given as 5.7%

K= 5.7% + 4.2% = 9.9%

Cost of Debt is the Yield to Maturity, which is given as 6.8%.

But this interest expense of 6.8% is tax deductible, so the interest expense of 6.8% is really 35% less

or (1- 0.35) * 6.8% = 0.65 * 0.068 = .0442 or 4.42%

Note: To find Hall Corp's weight average cost of capital (WACC)

we take the $Market Value of stock / ($Market Value of Stock + $Market Value of Debt)

which is $800,000/ ($800,000 + $459,000) = 0.635 rounded to three decimal places.

and we multiply this 0.635 * the cost of equity of 9.9% to get:

0.635 * 0.099 = 0.063 <-- rounded to two decimal places

The we take $Market Value of Debt / ($Market Value of Stock + $Market Value of Debt)

$459,000 / ($800,000 + $459,000) = 0.365 <-- rounded to three decimal places.

and we multiply this 0.365 * the after tax cost of debt of 4.42% to get

0.365 * 0.0442 = 0.016

We add the weighted cost of equity of 0.063 or 6.3% and

the weighted cost of debt of 0.016 o r 1.6% to get

6.3% + 1.6 = 7.9%

So the 7.9% is Hall Corp's weighted average cost of equity or WACC.

Now we can find the NPV of the project :

NPV = -$328,000 + $52,500/(1 + 0.079) + $155,000/ (1 + 0.079)^2 + $225,000/1 + 0.079)^3

= -$328,000 + $48,656.16 + $133,133.95 + $179,109.32

NPV = $32,899.43

Note that depending on how you round the intermediate steps you will get slightly different answers.

When I used Excel to do the calculations ( which rounds to 15 places) my answer was

NPV = $32,882.62