Finance Help: Check my answers Please?
Your uncle died last year and left you money in his will. You are to receive $70,000 three years from today (i.e., in time 3).
(a) What is the value of the inheritance today (in time 0) if the appropriate discount rate is 4% and you compound annually?
70,000/((1.04)^3)=62229.75
(b) If you invest the money when you receive it in time 3, how much will it grow to 25 years from today (i.e., in time 25) if you earn 4% each year?
70000+(1.04)^25= 186608.54
3. Your neighbor is buying a new recreational vehicle (RV). He has the following options to finance the RV:
I. Pays $42,000 today (in time 0)
II. Buy under a “no payments for two years” program by agreeing to pay $45,000 two years from today (in time 2).
III. Make 72 monthly payments over 6 years of $675 payable at the end of each month.
A) If the interest rate is 7% annually, calculate the present value of each option.
I) 42,000/(1.07)^0=42,000
II) 45,000/(1.07)^2=39304.74
(72*675=48600
III) 48600/(1.07)^6=32384.23
(b) How low does the interest rate have to fall before Option I is a better deal than Option II?
3% 45,000/(1.03)^2=42416.82
Answer:
a) What is the value of the inheritance today (in time 0) if the appropriate discount rate is 4% and you compound annually?
Correct: $62,229.75
(b) If you invest the money when you receive it in time 3, how much will it grow to 25 years from today (i.e., in time 25) if you earn 4% each year?
Wrong: You should deduct first the future value factor from time zero to time three.
(1.04^25 – 1.04^3) x 70000 = 107868.0632
3. Your neighbor is buying a new recreational vehicle (RV). He has the following options to finance the RV:
I. Pays $42,000 today (in time 0)
Same: $42000
II. Buy under a “no payments for two years” program by agreeing to pay $45,000 two years from today (in time 2).
Correct: $39,304.74 (best option)
III. Make 72 monthly payments over 6 years of $675 payable at the end of each month.
Wrong: You should use the present value of annuity at 7/12 percent for 72 periods which is 58.65444
$675 x 58.65444 = $39,591.75
(b) How low does the interest rate have to fall before Option I is a better deal than Option II?
Wrong: You may use interpolation for this. I used the ms excel’s IRR function for this one.
Find the rate that would equate $42000 to $39304.74 or vice versa.
6.42%. Therefore, rate should fall by 0.58%.