Lucky plans to finance a new project with $2M in bonds, $1M in preferred stock a

Question

Lucky plans to finance a new project with $2M in bonds, $1M in preferred stock and $5M in retained earnings. These proportions are the same as their target weights.

- The zero coupon bonds have a 5-year life and sold for $680.58.
- The preferred stock has a $2.70 annual dividend. The preferred stock has a price of $30 but issue costs are $3 per share.
- Lucky knows the Treasury bill rate is 3% and the market risk premium is 9%.   The common stock has a beta of 1.20. The tax rate is 30%.
- The project has a 5-year planning horizon. It costs $8,000,000 and generates $2,100,000 in after-tax cash flows every year for 4 years followed by an after-tax cash flow of $4,100,000 in year 5. Find the net present value of the project using the WACC.

Explanation / Answer

First, we calculate the WACC.

Cost of Equity, ke = Risk free rate (T-Bill rate) + Beta x Market Risk Premium

= 3% + (1.2 x 9%) = 13.8%

Cost of debt, kd = Yield on the zero coupon bond

= [(Par value / Market Value)1/Number of years to maturity] - 1

= [(1,000 / 680.58)1/5] - 1 = 8%

Cost pf preferred stock = Annual dividend / (Price - Issue Cost) = $2.70 / $(30 - 3) = 10%

Proportion of equity = $5M / $8M = 62.5%

Proportion of debt = $2M / $8M = 25%

Proportion of preferred stock = $1M / $8M = 12.5%

So, WACC = (62.5% x 13.8%) + [(25% x 8%) x (1 - 0.30)] + (12.5% x 10%) **

= 8.63% + 1.4% + 1.25% = 11.28%

** Interest on debt is tax-deductible, so cost of debt should be calculated post-tax basis.

Next, we calculate the NPV. The NPV is sum of all cash inflows and outflows, discounted at WACC of 11.28%.

The calculations are as follows.

From above table we see that NPV is $879,070.

Year Cash Flow Discount Factor @11.28% Discounted Cash Flow (PV) 0 -80,00,000 1.0000 -80,00,000 1 21,00,000 0.8986 18,87,132 2 21,00,000 0.8075 16,95,841 3 21,00,000 0.7257 15,23,940 4 21,00,000 0.6521 13,69,465 5 41,00,000 0.5860 24,02,693 NPV 8,79,070

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