Question

You have just received a windfall from an investment you made in a​ friend's business. He will be paying you $ 25,034 at the end of this​ year, $ 50,068 at the end of the following​ year, and $ 75,102 at the end of the year after that​ (three years from​ today). The interest rate is 10.2 % per year.

a. What is the present value of your​ windfall?

b. What is the future value of your windfall in three years​ (on the date of the last​ payment)?

Answer 1

a. Cashflow received at the end of this year = Cash flow for year 1 = CF1 = $25034

Cashflow received at the end of following year = Cash flow for year 2 = CF2 = $50068

Cashflow received at the end of year after that = Cash flow for year 3 = CF3 = $75102

Interest rate = r = 10.2%

Present value of a cash flow = Cash flow / (1+r)^{no of years}

So Present value of Windfall = Sum of present value of cash flows for year 1 to year 3 discounted at 10.2%

= CF1 / (1+ r)¹ + CF2 / (1+r)² + CF3 / (1+r)³ = 25034 / (1+10.2%)¹ + 50068 / (1+10.2%)² + 75102 / (1+10.2%)³ = 25034 / (1.102)¹ + 50068 / (1.102)² + 75102 / (1.103)³ = 25034 / 1.102 + 50068 / 1.214404 + 75102 / 1.338273208 = 22716.8784 + 41228.4544 + 56118.5859 = 120063.9187 = 120063.92

Hence Present value of windfall = $12006.92

b. We know that Future value of a cash flow in three years = Cash flow (1+r)^{no of years of end of year 3}

Sp Future value of windfall in three years = CF1(1+r)² + CF2(1+r)¹ + CF3(1+r)⁰ = 25034(1+10.2%)² + 50068(1+10.2%)¹ + 75102(1+10.2%)⁰ = 25034 x 1.214404 + 50068 x 1.102 + 75102 x 1 = 30401.3897 + 55174.9360 + 75102 = 160678.3257 = 160678.33 (rounded to two decimal places)

Future value of windfall in three years = 160678.33