Question

1. Welma wants to buy an elephant but she does not currently have the 14,000 required to buy the type of elephant she wants.

1. If she hopes to buy the elephant at this same price in three years, how much does she need to invest in 5% annually compounding T-bills at this moment in time to have enough money in three years? (Online fill in 1)
2. Assume that in three years elephants now cost $16,000. If elephants are good representations of current inflationary pressures. What is the effective yearly real rate of return on the T-bills?(Online fill in 2)

1. Jack and Diane, grew up in the heartland, have now been married for 20 years and would like to invest some money. Assume the risk free rate is 2% annually. They take a test that rates their individual risk preference. Jack is given a 5 and Diane a 2.(this is A in the equation 5.15 in the book) A- Which investment can the couple agree on, that it is better than the risk free asset? (online fill in 3) B- Using the stock that Jack and Diane have chosen in part B of question find the optimal allocation between risky(y) and risk free(1-y) investments for each person, with no shorting. What is the optimal y for Jack?(online fill in 4)

Answer 1

Ans A: Cost of elephants 14000 Welma will buy the elephants at this value in three years thus 14000 is our future value of elephants; Rate = 5% p.a. Time = 3 years. to find out how much Welma needs to invest at this moment in time we will find the Present Value using the formula PV= FV / (1+rate)^n = 14000 / (1+0.05)^3 = 12093.73. Thus Welma needs to invest 12093.73 at this moment in time to have enough money in 3 years to buy the elephant.

And B: Elephants cost in 3 years is $16000 we take the Present Value of elephant deduced in the answer A above i.e. 12093.73 to know the real rate of return on T-bills we would first found the rate at which 12093.73 will become 16000 in 3 years. For this we will be using the RATE function in excel i.e. = RATE(nper,,PV,-FV,0) where nper = 3; PV= 12093.73 and FV=16000 after substituting the variables in the formula we would get =RATE(3,,12093.73,-16000,0) = 9.78%. Note this rate is with inflationary effect.

We will find the Rate of inflation by assuming that 14000 is the value of elephant without inflation effect now if it becomes 16000 in 3 years the only reason is the inflation rate. To find the inflation rate we would again use the RATE function in excel i.e. = RATE(nper,,PV,-FV,0) where nper = 3; PV= 14000 and FV=16000 after substituting the variables in the formula we would get =RATE(3,,14000,-16000,0) = 4.55%. Note this rate is inflation rate.

Thus the real rate of return is Nominal Interest Rate = 9.78% less Inflation rate = 4.55% therefore we would get = 9.78 - 4.55 = 5.23%

To answer Jack and Diane question we need more information about equation 5.15 of the book.