Question

i dont know how to do (b), the answer is on the second picture but i dont get why it is discounted back by (1+ke)^n insdead of (1+g)^n, thanks a lot!

Problems Eo=3 Nano Technologies Ltd recently earned $3.00 per share and has a history of paying out 40% of earnings as dividends. This payout ratio is expected to continue in the foreseeable future. Also, Nano's earnings and dividends per share are expected to grow at a constant annual rate of 5 percent forever. es x = 0 a) Po - 9 What price should this stock sell for today if investors expect a 12% rate of return? - KECHG Your colleague, Noah Tall has suggested that perhaps a constant growth rate of 5 percent in dividends and earnings is too optimistic. He suggests that it is more likely that earnings would initially decline at a rate of 10 percent per year during the next 3 years in view of the long development period for Nano's recent high technology venture and then grow at the previously estimated rate of 5 percent per year. Assuming the dividend payout ratio remains unchanged at 40%, reestimate Nano's price using Noah's assumptions. Analyze the sensitivity of the price estimates to the assumptions made. (No calculations required.) Suppose ABC Ltd needs funds for 180 days only, and decides to raise the money by discounting a bank bill. ABC Ltd immediately draws a 180-day bill for $500,000 and this is sold into the market to yield 9.58%. What are the proceeds from discounting the bill?

Ke denotes tge required rate of return for equity holders

Answer 1

b) g or growth rate takes some value like earning or dividend in to future. In future generally earnings and dividends grow by the rate of growth. so to get the future value of earnings or dividends, these values are multiplied by 1+growth rate. to know the present value of these future earnings and dividends, we divide those values by 1+required rate of return.

required rate of return is the return an investor wants for his investment. Future value of investment incomes are discounted by required rate of return so that we can know if present value of future incomes are more than our investment. If we discount these future incomes with growth rate then present value of these future incomes will be higher than investment because growth rate is lower than required rate of return.

but in reality our analysis will be incorrect and actual return on our investment will negative because if we have used a discount rate which is lower than our required rate of return. required rate of return is the minimum return an investor wants.

Year 1 earnings = $3*(1-decline in growth rate)= $3*(1-0.10) = $3*0.90 = $2.7

Year 1 dividend = year 1 earning*dividend payout rate = $2.7*40% = $1.08

Year 2 earnings = year 1 earnings*(1-0.10) = $2.7*(1-0.10) = $2.7*0.90 = $2.43

Year 2 dividend = $2.43*40% = $0.36

Year 3 earnings = year 2 earnings*(1-0.10) = $2.43(1-0.10) = $2.43*0.90 = $2.187

Year 3 dividend = $2.187*40% = $0.8748

Earnings year 4 and beyond = Year 3 earning*(1+growth rate) = $2.187*(1+0.05) = $2.187*1.05 = $2.29635

Dividend year 4 and beyond = $2.29635*40% = $0.91854

Price of stock = Year 1 dividend/(1+required rate of return)¹ + Year 2 dividend/(1+required rate of return)² + Year 3 dividend/(1+required rate of return)³ + Terminal value/(1+required rate of return)³

Terminal value = Dividend year 4 and beyond/Required rate of return - growth rate = $0.91854/0.12 - 0.05 = $0.91854/0.07 = $13.122

Terminal value is calculated at the end of year 3 using year 4 and beyond dividend. so it will be discounted for 3 years only.

Price of stock = $1.08/1.12 + $0.36/1.12² + $0.8748/1.12³ + $13.122/1.12³

Price of stock = $1.08/1.12 + $0.36/1.2544 + $0.8748/1.404928 + $13.122/1.404928 = $0.96 + $0.29 + $0.62 + $9.34 = $11.21