Ten years ago. Video Toys began manufacturing and selling coin-operated arcade g

Question

Ten years ago. Video Toys began manufacturing and selling coin-operated arcade games. Dividends are currently $ 1.50 per share, having grown at a 15 percent compound annual rate over the past 5 years. The growth rate is expected to be maintained, for the next three years after which dividends are expected to grow at half that rate for 3 years. Beyond that time, Video Toys dividends are expected to grow at 5 percent per year. What is the current value of a share of Video Toys common stock if your required rate of return is 18 percent.

A $1230 investment has the following expected cash returns

year ($)

1 800

2 200

3 400

Compute the internal rate of return for the project

Explanation / Answer

Rate of Return Ks = 18%, Find P0 Step 1. Calculate the dividends expected at the end of each year during the supernormal growth period. Y1 & y2 & Y3 (gn=15%) Step 1a. Calculate the dividends expected at the end of each year during the next supernormal growth period. Y4 & y5 & Y6 (gn1 = 7.5%) Step 2. The price of the stock is the PV of dividends from Time Y1 to infinity, so in theory we could project each future dividend, with the normal growth rate, g = 5%, used to calculate D7 and subsequent dividends. However, we know that after D3 has been paid, which is at Time Y3, the stock grows at gn1=7.5% for 3 yrs and then becomes a constant growth stock in Y7. Therefore, we can use the constant growth formula to find P6, which is the PV of the dividends from Time Y7 to infinity as evaluated at Time Y7. First, we determine D3 & D6 for use in the formula, and then we calculate P6 as follows: P6=D7/(Ks-g). Step 3. Now that the cash flows have been placed on the time line, we can discount each cash flow at the required rate of return, ks=18%. We could discount each cash flow by dividing by (1.18)^t, where t=1 for Time 1, t=2 for Time 2. This produces the PVs shown to the left below the time line, and the sum of the PVs is the value of the supernormal growth stock P0. 0 gs=15% 1 gs=15% 2 gs=15% 3 gs=7.5% 4 gs=7.5% 5 gs=7.5% 6 g=5% 7 |------------|-----------|-----------|------------|----- -----|-----------|---------|------- D0=1.5 D1=1.725 D2=1.984 D3=2.28 D4=2.45 D5=2.64 D6=2.84 D7=2.98 P6=22.92 a. Terminal or Horizon date is at end of 6 Yrs when Non-constant growth stops. b. Do=1.5, gs = 15% = 0.15, N=3 yrs, g=5%, Ks=18% So D1 = Do(1+gs) = 1.5(1+15%) = $1.725 D2 = D1(1+Gs) = $1.725*1.15 = $1.984 D3 = D2*(1+Gs)= $1.984*1.15 = $2.28 After 3 yrs, supernatural growth is over & next cylce of supernatural growth starts at 7.5% growh rate for 3 yrs and after that normal growth of 5% starts till infinity So D4 = D3(1+gs) = 2.28*(1+7.5%) = $2.45 So D5 = D4(1+gs) = 2.45*(1+7.5%) = $2.64 So D6 = D5(1+gs) = 2.64*(1+7.5%) = $2.84 When normal growwth starts, D7 = D6(1+g) = 2.84*(1+5%) = $2,98 So P6 = D7/(Ks-g) = 2.98/(18%-5%) = $22.92 So P0 = D1/(1+Ks)^1 + D2/(1+Ks)^2 + D3/(1+Ks)^3+ D4/(1+Ks)^4+ D5/(1+Ks)^5+ D6/(1+Ks)^6 + (P6+D7)/(1+Ks)^7 ie P0 = 1.725/1.18 + 1.984/(1.18)^2 + 2.28/(1.18)^3 + + 2.45/(1.18)^4+ 2.64/(1.18)^5+ 2.84/(1.18)^6+(22.92+2.98)/(1.18)^7 ie P0 = $15.87 So current price of Stock is $15.87 .................ANS IRR using excel function is IRR(CFs) = IRR(-1230,800,200,400) = 8%.....ANS

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