Corporate Finance Practice Exam — Free

The constant-growth (Gordon) model prices a share as the present value of a dividend stream that grows at rate $g$ forever:

$$P_0 = \frac{D_1}{r - g}$$

The model needs the next dividend, $D_1$, not the one just paid. Because the $2.00 was paid a moment ago, the next dividend is one growth step ahead:

$$D_1 = D_0(1 + g) = 2.00 \times 1.05 = 2.10$$

Now substitute, keeping the rates as decimals:

$$P_0 = \frac{2.10}{0.11 - 0.05} = \frac{2.10}{0.06} = 35.00$$

The stock is worth $35.00 per share.

Check by reasoning from the result: at $35.00 the dividend yield is $D_1 / P_0 = 2.10 / 35.00 = 6\%$, and adding the 5% capital-gains yield from growth gives the 11% total return investors require, so the price is consistent with the model.

Option A ($33.33) is the most common error: it uses the dividend just paid, $D_0 = 2.00$, in the numerator instead of growing it forward one year. Option C ($19.09) discounts $D_1$ at $r$ alone, as if the dividend were a level perpetuity with no growth. Option D ($13.13) adds the growth rate to the discount rate instead of subtracting it.

Answer: B — $35.00.

(a) Required return. The CAPM says the required return equals the risk-free rate plus a risk premium proportional to beta:

$$E(R_i) = R_f + \beta_i\,[E(R_m) - R_f]$$

The bracket is the market risk premium, which must be built from the two rates given: $9\% - 3\% = 6\%$. A common slip is to multiply beta by the 9% market return itself. Substituting:

$$E(R_i) = 3\% + 1.4 \times 6\% = 3\% + 8.4\% = 11.4\%$$

Lakeshore carries 1.4 times the market's systematic risk, so it must offer 1.4 times the market premium on top of the risk-free rate: 11.4%.

(b) Over- or undervalued. The security market line (SML) plots required return against beta. The analyst's forecast of 10.5% is the return investors expect at the current price. Because 10.5% is less than the 11.4% the stock's risk demands, the stock plots below the SML: its price is too high for the return it delivers, so it is overvalued. Investors acting on this would sell, pushing the price down until the expected return rises to 11.4%. (If the forecast had been above 11.4%, the stock would plot above the line and be undervalued.)

Answer: (a) 11.4%; (b) overvalued, because its 10.5% expected return is below the 11.4% CAPM-required return.

(a) NPV. Discount each cash flow at 10% and subtract the initial outlay:

$$\begin{aligned} \text{NPV} &= -150{,}000 + \frac{55{,}000}{1.10} + \frac{65{,}000}{1.10^2} + \frac{70{,}000}{1.10^3} \\ &= -150{,}000 + 50{,}000.00 + 53{,}719.01 + 52{,}592.04 \\ &= 6{,}311.05 \end{aligned}$$

The NPV is about $6,311: the project earns the 10% investors require and adds roughly $6,300 of value on top.

(b) IRR. The IRR is the rate that makes NPV zero. Because NPV is positive at 10%, the IRR is higher. Try 12%:

$$\text{NPV}_{12\%} = -150{,}000 + 49{,}107.14 + 51{,}817.60 + 49{,}824.62 = 749.36$$

Try 13%:

$$\text{NPV}_{13\%} = -150{,}000 + 48{,}672.57 + 50{,}904.53 + 48{,}513.51 = -1{,}909.39$$

The sign changes between 12% and 13%, so interpolate:

$$\text{IRR} \approx 12\% + \frac{749.36}{749.36 + 1{,}909.39} \times 1\% = 12\% + 0.28\% \approx 12.3\%$$

(c) Payback. Cumulative cash flow after year 2 is $55,000 + $65,000 = $120,000, leaving $30,000 to recover from year 3's $70,000:

$$\text{Payback} = 2 + \frac{30{,}000}{70{,}000} \approx 2.43 \text{ years}$$

(d) Decision. Accept the project: the NPV rule says take any project with NPV above zero, and the IRR rule agrees because 12.3% exceeds the 10% cost of capital. For a conventional project like this one (one outflow followed by inflows) the two rules always give the same accept-or-reject answer. Payback is not a decision rule here because no cutoff was specified, and it ignores both the time value of money and cash flows after the cutoff.

Answer: (a) NPV ≈ $6,311; (b) IRR ≈ 12.3%; (c) payback ≈ 2.43 years; (d) accept, since NPV > 0 and IRR > 10%.