Tim has preferences over consumption in period 1 and 2 of the form . The price of consumption is $1 in both periods. He has $10,000 in the bank now and is trying to decide between two different investment opportunities, A and B.
A: invest $4,000 in period 1 and receive $8,000 in period 2.
B: invest $2,000 in period 1 and receive $5,000 in period 2.
If Tim can borrow and save at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $4000 if he chooses A, or $2000 if he chooses B.) Show your analysis
Given your answer in (a), how much will he consume in each period?
Given your answer in (a), how much will he consume in each period if now his saving interest rate is 20% and the borrowing rate is still 50%? Show your analysis.
Underlying objective behind each investment is to maximize the Net Present Value (NPV). Using a discount rate of 50%, the NPVs of both the investments is:
1) NPV of A = – 4000 + 8000 / 1.5 = $ 1,333.33
2) NPV of B = – 2000 + 5000/1.5 = $ 1,333.33
SInce the NPV in both the cases is same, the next step would be to compare the rate of returns of two investments.
RoI for A = (8000 – 4000) / 4000 = 100 %
RoI for B = (5000 – 2000) / 2000 = 150 %
Tim will choose investment opportunity B because fir the same NPV, Tim receives higher RoI for investment B.
Tim will consume $ 2000 in period 1 and $ 4000 in period 2 because these investments provides higher returns than keeping the money in bank as the savings interest rate is 50%. Tim will be better off by investing $ 2000 in period 1 and $ 4000 in period 2.
The answers will still be the same if the interest rates change because Tim has enough money in bank and there is no need to borrow. Also there are limits on investment amounts ($ 4000 in A and $ 2000 in B)