Beverly's is a retail chain selling the latest fashions through its outlets located in various neighborhood malls. Clothing Galore is a wholesaler that buys from textile mills and sells to retail outlets. Beverly's has a cost of capital of 13.6 percent, while Clothing Galore's cost of capital is 17.8 percent. Both firms are considering opening a retail outlet in a gigantic new mall. Both proposals are quite similar in design and have basically the following financial features: an initial cash outlay of $2.7 million, a projected five-year life with no salvage value, and cash inflows of $845,000 a year for the life of the project. Which firm or firms, if either, should open a retail outlet in the new mall?

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BlackTom AI · Accepted Answer

We start by restating the scenario to ensure clarity: Beverly's and Clothing Galore are evaluating identical projects with an initial outlay of 2.7 million, a five-year life, no salvage value, and annual cash inflows of 0.845 million. Each firm uses its own cost of capital as the discount rate: Beverly's at 13.6% and Clothing Galore's at 17.8%. The key decision metric here is the net present value (NPV) of the project for each firm, calculated as NPV = -Initial Outlay + Present Value of Cash Inflows.

Option 1: Neither Beverly's nor Clothing Galore. This choice would be correct only if both NPVs were negative or the investment was otherwise unattractive for both firms. To evaluate, we compute NPVs for each firm’s cash flows using their respective discount rates. If either NPV is positive, this option is incorrect.

Option 2: Clothing Galore only. If this were true, Clothing Galore would have a positive NPV while Beverly's would have a negative NPV. We need to compare the present value of the five annual inflows to the 2.7 million outlay at each discount rate to see which, if any, yields a positive NPV.

Option 3: Both Beverly's and Clothing Galore. This would require both NPVs to be positive. Given the higher cost of capital for Clothing Galore, achieving a positive NPV for both is unlikely if one is close to or below the break-even point.

Option 4: Beverly's only. This would be true if Beverly's project has a positive NPV at 13.6% while Clothing Galore's has a negative NPV at 17.8%.

Now, calculate the present value factor for an annuity (PVIFA) for each firm, using the formula PVIFA(r, n) = [1 - (1 + r)^-n] / r, with n = 5 and r equal to each firm's cost of capital.

For Beverly's (r = 13.6% = 0.136): (1 + r)^5 ≈ 1.136^5. Approximating, 1.136^2 ≈ 1.290, 1.136^3 ≈ 1.466, 1.136^4 ≈ 1.666, 1.136^5 ≈ 1.892. Thus (1 + r)^-5 ≈ 1 / 1.892 ≈ 0.529. Then PVIFA ≈ [1 - 0.529] / 0.136 ≈ 0.471 / 0.136 ≈ 3.46. Present value of inflows ≈ 0.845 × 3.46 ≈ 2.93. NPV ≈ -2.70 + 2.93 ≈ +0.23 million. So Beverly's yields a positive NPV.

For Clothing Galore (r = 17.8% = 0.178): (1 + r)^5 ≈ 1.178^5. Estimating, 1.178^2 ≈ 1.387, 1.178^3 ≈ 1.635, 1.178^4 ≈ 1.928, 1.178^5 ≈ 2.274. Therefore (1 + r)^-5 ≈ 1 / 2.274 ≈ 0.440. PVIFA ≈ [1 - 0.440] / 0.178 ≈ 0.560 / 0.178 ≈ 3.15. Present value of inflows ≈ 0.845 × 3.15 ≈ 2.66. NPV ≈ -2.70 + 2.66 ≈ -0.04 million. So Clothing Galore yields a slightly negative NPV.

Interpreting these results, Beverly's plan has a positive NPV, making it financially attractive at its cost of capital, while Clothing Galore's plan has a negative NPV, making it unattractive at its higher cost of capital. The comparison shows that at the given inputs, one firm’s project is favorable and the other’s is not.

Putting the pieces together, the option that aligns with Beverly's project yielding a positive NPV and Clothing Galore yielding a negative NPV corresponds to the scenario described by the choice stating that Beverly's is the viable option while Clothing Galore should not proceed. The remaining options would require conditions (positive NPVs for both, or a positive NPV for Clothing Galore only) that are inconsistent with the computed NPVs above.

Note on sensitivity and rough arithmetic: the PVIFA values above are approximate due to rounding during intermediate steps. Small changes in the discount rate or cash flow timing can shift the NPVs marginally, but the qualitative result (Beverly's positive, Clothing Galore negative) is robust given the sizable difference in discount rates relative to the cash inflow stream and initial outlay.

FIN 220 01 Final Exam _ Fall 2025

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