2. An investor is planning to make a new investment: it will pay $500 every year
ID: 1171047 • Letter: 2
Question
2. An investor is planning to make a new investment: it will pay $500 every year starting in 2018 for 3 years. The nominal discount rate for this investment is 15%. The price index is 1.13 in 2017, 1.17 in 2018,1.22 in 2019, and 1.30 in 2020 2.1. Find the rates of inflation: 2.1.1. From 2017 to 2018 2.1.2. From 2017 to 2019 2.1.3. From 2017 to 2020 2.2. Find the real present value for the returns from the investment. Show work. (Hint: use the inflation rates found above) 2.3. Suppose instead the investor buys stock, which will bring $50 in one year and will be sold at face value of $1,000. Find the nominal Present Value of the stock.Explanation / Answer
Inflation rate = Price index at Yr 2 - Price index at Yr 1/Price Index at Yr 1 Inflation rate from 2017 to 2018 = 1.17-1.13/1.13 3.54% Inflation Rate from 2018 to 2019 = (1.22-1.17)/1.17 4.27% Inflation Rate from 2019 to 2020 = (1.30-1.22)/1.22 6.56% Inflation rate from 2017 to 2019 = (1.22-1.13)/1.13 7.96% Inflation rate from 2017 to 2020 = (1.30-1.13)/1.13 15.04% Real Rate of Return = (1+Nominal rate of return/1+inflation rate) - 1 Real rate of return in 2018 ((1+0.15)/(1+0.035398)) - 1 0.110684008 Real rate of return in 2019 ((1+0.15)/(1+0.042735)) - 1 0.102868898 Real rate of return in 2020 ((1+0.15)/(1+0.065574)) - 1 0.079230537 Year Cash Inflow( In$) Discount factor = 1/1+Real return^n Present Value (In $) 2018 500 1/(1+0.110684)^1 0.900346 450.17 2019 500 1/(1+0.102869)^2 0.822152 411.08 2020 500 1/(1+0.079231)^3 0.79553 397.77 Present value of Investments (In $) 1,259.01 If investor invests in stock, than the nominal present value would be PV = 50(1/1.15^1)+1000(1/1.15^1) PV = 50(1/1.15^1)+1000(1/1.15^1) 50*0.8696+1000*0.8696 913.08 The Nominal present value of stock is $ 913.08
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