PriceSmart Shops has $50Min assets, $35 in debt, and $10M in common stock. The d

Question

PriceSmart Shops has $50Min assets, $35 in debt, and $10M in common stock. The dividend preferred stock is $1.50 per share and its price is $25 and has a 5% commission. The expected dividend on common stock is $1.00 per share and its price is $20. The grown of common stock is 3.5% All of Price Smart's bonds are selling for $925 and have a future value of $1,000. The bonds have 5 years left until maturity and pay a 5% coupon semi-annually. The current tax rate is 34%. PriceSmart is considering the rights of a product to sell in their stores that costs $500,000. The investemnt is expected to generate $95,000 in the first year and then increase by 12% annually for the next four years. Assume all other information remains teh same. What is the discounted payback period for this investment?

Explanation / Answer

1. Cost of preferred stock = Preferred stock dividend/(Market price of preferred stock – Commission) = $1.50/$25(1-0.05) = $1.50/$23.75 = 0.0632 = 6.32%

2. Cost of Equity

Price per share of common stock = Dividend for next year/(Cost of equity – Growth rate)

$20 = {$1*(1+0.035)} / (Cost of equity – 0.035)

Cost of equity – 0.035 = $1.035/$20 = 0.0518

Cost of equity = 0.0518 + 0.035 = 0.0868 = 8.68%

3. Cost of debt

Value of debt = Present value of coupon payments + Present value of face value

Present value of annuity = Annuity * {1 – (1+r)-n}/r

Present value of remaining 10 semi-annual coupon payments = $25* {1 – (1+r)-10}/r

Present value of face value = $1,000/(1+r)10

$925 = $25* {1 – (1+r)-10}/r + $1,000/(1+r)10

Solving above we get, r = 0.0340 = 3.4%

This is semi-annual rate.

Annual rate = 3.40% * 2 = 6.80%

Cost of debt after tax = 6.8% * (1 – tax rate) = 6.80% * (1 – 0.34) = 4.42%

4.

Value of preferred stock = Assets – Debt – common stock = $50 million - $35 million - $10 million = $5 million

Value (in millions)

Weights

Cost of capital

Weighted cost of capital

Preferred stock

$ 5

          0.10

6.32%

0.63%

Equity

$ 10

          0.20

8.68%

1.74%

Debt

$ 35

          0.70

4.42%

3.09%

$ 50

5.46%

Hence rate of return = Weighted average cost of capital = 5.46%

5.

Year

Cash flows

Present value factor @ 5.46%

Present value of cash flows

Cumulative cash flows

1

$ 95,000.00

           0.9482

$ 90,079.00

$ 90,079.00

2

$ 106,400.00

           0.8991

$ 95,664.24

$ 185,743.24

3

$ 119,168.00

           0.8526

$ 101,602.64

$ 287,345.88

4

$ 133,468.16

           0.8084

$ 107,895.66

$ 395,241.54

5

$ 149,484.34

           0.7666

$ 114,594.69

$ 509,836.23

Payback period = 4 years + {($500,000 - $395,241.54)/$114,594.69} = 4 years + 0.91 = 4.91 years

Value (in millions)

Weights

Cost of capital

Weighted cost of capital

Preferred stock

$ 5

          0.10

6.32%

0.63%

Equity

$ 10

          0.20

8.68%

1.74%

Debt

$ 35

          0.70

4.42%

3.09%

$ 50

5.46%

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