Question

Twenty-one years later, the firm has 20 stores throughout 7 east coast states, of which 10 are operated by the company and 10 by franchisees. Each store was built to the same specifications for both interior and exterior design. Locations were chosen in heavily African-American populated areas since their success depended greatly upon serving a target market of customers with the resources to purchase the firm’s art products. Inventory items were standardized into the three categories, and advertising focused on one of the three product themes. Prospective franchisees signed a document that was designed to keep sales of items, locations and other details standard irrespective to their geographical location, and each new location required an initial payment of $10,000. In addition, franchisees were obligated to a royalty of 5% of gross sales, and each franchisee had to spend at least 2% of gross receipts on local advertising. The firm believed that properly trained employees were the key to success; therefore, managers and company trainees were required to attend a two-week program covering all aspects of the company’s operations. This case begins in June, 2010 when Mr. Smith started preparing to complete his analysis for the construction of five new company-owned stores where the sizes have not yet been determined. Mr. Smith and his management team believe that a larger capacity store with capacity to handle $100,000 in product inventory would be more profitable than the present stores where inventory capacity is $70,000. The company faces two choices that Mr. Smith must evaluate with your assistance: continue with the current smaller sized stores, or select larger stores for the firm’s strategic growth or construction plan. The initial cost will be $2,100,000 for each of the smaller sized stores and $3,700,000 for each of the five larger ones. Projected present value of cash flows for the smaller units projected for the firm’s five-year strategic plans are $450,000 for each year while the projected cash flows for the larger units are projected to be $740,000 per year. Because the projects must be financed from different sources, unfortunately, financing costs will be different. Mr. Smith’s data indicates that the current and projected 120-day treasury bill rate is 9.75% and the firm’s expected market return is 12.5% for the plan period. The beta for the African art industry and the planned new stores is 1.15. However, the bond rates for the projects are 10% for the smaller stores and 12.7% for the larger store funds. Thus, the details have been provided for the analysts, namely you, to:

1. Determine the capital asset pricing model rate for the firm.

2. Combine that rate with the specific debt rates for each store model, using a tax rate of 34%.

3. Determine the weighted average cost of capital (WACC) for each project.

4. Find the net present value (NPV) for each alternative purchase.

5. Use the NPV and profitability index analyses (because each project will have a different WACC rate) to advise/convince Mr. Smith of your selection of the most desired, profitable project for the company.

Answer 1

1. Capital Asset Pricing Model rate for the firm = Risk free return + Beta ( Market Return - Risk free Return)

CAPM rate (K_e) = 9.75 + 1.15 * (12.5 - 9.75)

CAPM rate (K_e) = 12.9125%

2. For small sized stores, bond rate = 10% (pre tax)

Post tax bond rate = bond rate pre tax - tax rate

Post tax bond rate [ K_d (1 - tax) ] = 10 - 34% = 6.6%

So now we get K_e + K_d (1 - tax) = 12.9125+6.6 = 19.5125%

For large sized stores,

bond rate = 12.7% (pre tax)

Post tax bond rate = bond rate pre tax - tax rate

Post tax bond rate [ K_d (1 - tax) ] = 12.7 - 34% = 8.382%

So now we get K_e + K_d (1 - tax) = 12.9125 + 8.382 = 21.2945%

3. Weighted average cost of capital for both projects on the assumption that they were financed using 50% debt and 50% equity

WACC = Weight of equity* K_e + Weight of debt * [K_d (1 - tax)]

WACC for small stores = 0.5*12.9125 + 0.5*6.6 = 9.7563%

WACC for large stores = 0.5 * 12.9125 + 0.5 * 8.382 = 10.6473%

4. NPV = Present value of inflow - Present value of outflow [period = 5 year (given)]

NPV of each of small store = Present value of 450,000 each year for 5 years - 2100000 at discounting factor 9.7563%

NPV for each small store= $ 383,472.5

NPV of all 5 small stores = 383472.5*5 = 1,917,362.5

NPV of each of large store = Present value of 740,000 each year for 5 years - 3,700,000 at discounting factor 10.6473%

NPV of each of large store = $ 940,596

NPV of 5 large stores = 940596*5 = $ 4,702,980

5. NPV is a measure which helps us to decide which project gives the maximum present value of net inflow whereas profitability index analysis helps us to find inflow per dollar of outflow. Here in the given case, NPV of large store is more which indicates that larger store should be opted. Profitability of large store is also highest (i.e. Present value of inflow/ Present value of outflow) therefore Mr. Smith is advised to go for larger stores.