Question

Problem 4 1) JB Hanover has $170,000 to be invested for 6 years at 9%. Do the following (Use 4 decimal places) 1) 2) 3) Determine the future value Using the formula, solve for T to prove your answer in 1 Using the formula solve for R to prove your answer in 1 Your good friend will graduate Fall with honors her parents have decided to give her a gift with the following options. 1) $28,000 Now. 2) $7,000 per year for the next 5 years 3) $35,000 at the end of 5 years 4) An irregular cash flow streamm Year Cash flows 1) $8,000 2) $6,000 3) $5,000 4) $12,000 5) $6,000 Which should she choose if the interest rate is 9%? If an "Annuity Due was the 5th Option above, would your choice be different? If so, why?

Answer 1

Future value is the present value compounded by the interest rate for the estimated years.

JB Hanover has $170,000 to invest for 6 years at 9%.

Hence, PV=170,000., R=9%., T= 6

Future value = PV(1+R/100)^T

=170,000(1+0.09)^6

=285,107.

Solving for T:

285,107=170,000(1+0.09)^T

By trail and error method, we will get T=6

Solving for R:

285,107=170,000(1+R/100)^6

By trail and error method, we will get R=9%.

Hence, the answers are proved.

Choice of gift:

1) $28,000 now

2)$7,000 per year for next 5 years

Lets calculate the present value of this option discounting at 9%.

Year	Cashflow	DCF@9%	DCF
1	7,000	0.9174	6,422.02
2	7,000	0.8417	5,891.76
3	7,000	0.7722	5,405.28
4	7,000	0.7084	4,958.98
5	7,000	0.6499	4,549.52
Present value =			27,227.56

3)$35,000 at the end of 5 years

Lets calculate the present value of this option discounting at 9%.

DCF @ 9% for 5 years = 3.8897

PV=35,000/3.8897

= 9004.37.

4)Irregular cash flow stream

Lets calculate the present value of this option discounting at 9%.

Year	Cashflow	DCF@9%	DCF
1	8,000	0.9174	7,339.45
2	6,000	0.8417	5,050.08
3	5,000	0.7722	3,860.92
4	12,000	0.7084	8,501.10
5	6,000	0.6499	3,899.59
Present value =			28,651.14

Now out of these four options, option 4 has the highest value. So, it should be preferred.

If Annuity Due is taken as 5th option,

Note: As there is no information regarding the annuity amount, it is assumed that Option 2 is considered which is an annuity policy.

Then The PVF at 9%=4.2397

PV= 7,000*4.2397

= 29677.90.

Then , option 5 will be preferred because it has highest present value. The reason is that annuity due starts immediately which increases the present value because of no discounting for the first payment.