Bob suggested Brody consider using the “discounted payback period approach” and
ID: 2760452 • Letter: B
Question
Bob suggested Brody consider using the “discounted payback period approach” and the “Profitability Index Model (PI)”. Bob asked Brody, what is you cost of capital? Brody said, I can raise half from stock (about a 4% cost) and the remaining half from bonds (about a 5% cost). Brody estimated the initial cash outlay for option 1 was $7,000,000 and for option 2, $5,500,000. Bob said first figure out you cost of capital and use that as your discount rate. He then said to take into consideration the added risk, Bob said an additional 5% to option 1, and 4% to option 2. Brody estimated the annual cash flow for the two options.
Cash Flow Year Option 1 = 2,500,000 per year for 5 years
Option 2 = year 1 $1,500,000 year 2 $2,500,000 year 3 $3,500,000 year 4 $4,500,000 year 5 $5,500,000
Answer the following questions for Brody
Which option is the most acceptable using the discounted payback period? Why or why not.
Using the PI model, is the project acceptable? Why or why not? Because option 2 is a higher risk then option1, Bob suggest that Brody use a higher discount rate for option 2 (use a 6% discount rate) but for option 1 use the same rate used as for the discounted payback period calculation.
Does either of the two approaches change your decision about opening a new sports retail store? What would you suggest to Brody.
Explanation / Answer
Option 1:
Weighted Average Cost of Capital = (50% x 4%) + (50% x 5%) = 4.5% + 5% (Risk Premium) = 9.5%
Cash Outflow = $7,000,000
Discounted Cash Inflows:
Year 1 = $2,500,000 / (1 + 0.095) = $2,283,105.02
Year 2 = $2,500,000 / (1 + 0.095)2 = $2,085,027.42
Year 3 = $2,500,000 / (1 + 0.095)3 = $1,904,134.63
Year 4 = $2,500,000 / (1 + 0.095)4 = $1,738,935.73
Year 5 = $2,500,000 / (1 + 0.095)5 = $1,588,069.16
Recovered amount at the end of year 3 = $6,272,267.07
Total Payback Period = Year 3 + [($7,000,000 - $6,272,267.07)/($1,738,935.73)] = 3.4185 Years
Option 2:
Weighted Average Cost of Capital = (50% x 4%) + (50% x 5%) = 4.5% + 4% (Risk Premium) = 8.5%
Cash Outflow = $7,000,000
Discounted Cash Inflows:
Year 1 = $1,500,000 / (1 + 0.085) = $1,382,488.48
Year 2 = $2,500,000 / (1 + 0.085)2 = $2,123,638.22
Year 3 = $3,500,000 / (1 + 0.085)3 = $2,740,178.34
Year 4 = $4,500,000 / (1 + 0.085)4 = $3,247,084.28
Year 5 = $5,500,000 / (1 + 0.085)5 = $3,657,749.83
Recovered amount at the end of year 3 = $6,246,305.04
Total Payback Period = Year 3 + [($7,000,000 - $6,246,305.04)/($3,247,084.28)] = 3.2321 Years
Profitability Index = Present Value of Future Cash Flows / Initial Investment
Option 1:
=> $9,599,271.97/$7,000,000 = 1.371325
Option 2:
=> $ 13,151,139.15/ $7,000,000 = 1.878734
So, this method again suggests to go with option 2.
Earlier the discount rate for option was 8.5% with 4.5% WACC, which will increase to 10% now.
So, with new discount rates for option 2:
Discounted Cash Inflows:
Year 1 = $1,500,000 / (1 + 0.10) = $1,363,636.36
Year 2 = $2,500,000 / (1 + 0.10)2 = $2,066,115.70
Year 3 = $3,500,000 / (1 + 0.10)3 = $2,629,601.80
Year 4 = $4,500,000 / (1 + 0.10)4 = $3,073,560.55
Year 5 = $5,500,000 / (1 + 0.10)5 = $3,415,067.28
Recovered amount at the end of year 3 = $6,059,353.87
Total Payback Period = Year 3 + [($7,000,000 - $6,059,353.87)/($3,073,560.55)] = 3.3060 Years
Option 2:
=> $ 12,547,981.70/ $7,000,000 = 1.79257
Even with the increased discount rates, option 2 provides with lesser payback period and higher profitability index compared to option 1, so the option 2 should be opted.