Question

Terri Allessandro has an opportunity to make any of the following investments: P . The purchase price, the lump-sum future value, and the year of receipt are given below for each investment Terri can earn a rate of return of 12% on investments similar to those currently under consideration. Evaluate each investment to determine whether it is satisfactory, and make an investment recommendation to Terri. The present value, PV, at 12% required return of the income from Investment A is $ . (Round to the nearest cent.) i Data Table 19 Investment Purchase Price Future Value Year of Receipt $11,856 $24,000 $474 $3,000 $3,499 $12,000 10 $694 $19,000 (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Enter your answer in the answer box and then click Check Answer

Answer 1

The table shows PV of all investment at 12% rate of return.

The purchase price of Investment A is less than the present value so it is the recommended investment as the returns are as required. For all others the purchase price is more than the present value of the investment so investment A should be recommended.

PV of income from investment A is $ 12,159

A B F G 1 2 Investment 3 A 4 B 5c 6 D 7 Purchase price Future value $ 11,856.00 $ 24,000.00 $ 474.00 $ 3,000.00 $ 3,499.00 $ 12,000.00 $ 694.00 $ 19,000.00 12% Year of receipt PV @12% 6 $ 12,159.15 19 $ 348.32 10 $ 3,863.68 39 $ 228.69 =C3/(1+$E$1)^D3 '=C4/(1+$E$1)^D4 =C5/(1+$E$1)^D5 =C6/(1+$E$1)^D6

For the next question we will use present value of annuity. The formula to determine the present value of an annuity:

P = PMT x ((1 – (1 / (1 + r) ^ -n)) / r)

Where

P = the present value of annuity

PMT = the amount in each annuity payment (in dollars)

R= the interest or discount rate

n= the number of payments left to receive

By doing the working we get PV of $ 4 million at end of each of next 30 years is $ 1,033,994.03

8 $ 40,00,000 7.50% $-10,33,994.03 9 Annual amount 10 Number of years 11 Discount rate 12 P= 13 14 P = PMTX ((1-(1/(1+r)^-n)) /r) 15 (1+r)^-n 16 1/(1+r)^-n 17 1-(1/(1+r)^-n) 18 (1-(1/(1+r)^-n)/r) 19 pmt* (1-1/(1+r)^-n)/o) 20 0.11422103 8.754955189 -7.754955189 -0.258498506 $ -10,33,994.03

The present value to $4 million received annually for 30 years is $ 1,033,994.03 so we suggest to take $69.25 million today as it is more than the PV of annual payments.