Question

11. An asset promises to pay $1,000 in each of the next two years.

a) What is its present value assuming the one-year rate of discount is 1.5% and the two-year is 2.2%?

b) What is its present value assuming both discount rates are 1.85%?

12. An asset promises to pay $60 in each of the next three years. Assume the rate of discount is 5% for each of the years.

a) Calculate its price the “long” way; by discounting each future cash flow and summing. b) Calculate its price using the annuity formula.

Answer 1

Answer 11a

PV of year 1 cashflow=1000/(1+1.5%)^1=1000/1.015=985.22

PV of year 2 cashflow=1000/(1+2.2%)^2=1000/1.022^2=1000/1.0445=957.40

Hence total PV=985.22+957.4=1942.62

Hence PV=$1942.62

Answer 11 b

PV of year 1 cashflow=1000/(1+1.85%)=1000/1.0185=981.84

PV of year 2 cashflow=1000/(1+8.5)^2=1000/1.085^2=1000/1 0373=963.99

Hence PV= 981.84+963.99=1945.83

Hence PV=$1945.83

Answer 12a

PV of year 1 cashflow=60/(1+5%)=60/1.05=57.14

PV of year 2 cashflow =60/(1+5%)^2=60/1.05^2=60/1.1025=54.42

PV of year 3 cashflow=60/(1+5%)^3=60/1.05^3=60/1.1576=51 83

Total PV=57.14+54.42+51.83=163.39

Hence PV=$163.39

Answer 12b

PV of annuity= A*(1-(1+r)^-n)/r

=60*(1-(1+5%)^-3)/5%

=60*(1-1.05^-3)/0.05

=60*(1-0.8638)/0.05

=60*0.1362/0.05

=163.39

Hence PV=$163.39