Question

a Jestion 1 Consider the following four independent cases and answer the questions. Show your work for partial creat when earned to be awarded. (Showing your work, if you are using a financial calculator motinoidea parameters you are using as inputs and what you are telling it to compute.) Time value of money factors are included in the exam instructions 5 points each part a. Doreen is 25 years old today. She invests $3,000 today and on every subsequent birthday until her son h retirement fund that ears 8% annual interest. How much will be in the find other birthday? b. Garion Corp. issues $1 million of bonds with a 4 stated interest rate that mature in nas sis and semiannually. The market rate of return for these bonds is 8%. How much wol Ganon male brebonsar issuance? - Art c. You have won a lawsuit that requires the defendant pay you $10000 per jurististalinens starting or year from today. A finance company has offered you $42.000 batay in exchange for these mens Should accept the offer? Why or why not? Assume an 8% discount rates ar e d. Drucal Corpestimates it will need $2 million to pay for enviamental kanpants on an is m e t the mine closes in six years. Al wants to make six annualmente stortiny buty so that I can $2 million at the end of six years. What is the amount of the annulment the train de staan return? 2

Answer 1

a) Doreen is 25 year old , she invest $3000 today and will invest on eery birthday till 64th birth day at rate of 8% annual interest rate

Thus, lets find amount at end of 64th birthday

FV(Annuity due) =A [(1+r)^n - 1/ r] x (1+r)

r= rate of interest = 8%

n = 64-25 = 39

A = 3000

FV(Annuity due) = 3000[(1+8%)^39 - 1 /8%] x (1+8%)

=3000 [(1+0.08)^39 - 1/ 0.08] x (1+0.08)

=3000[(1.08)^39 - 1 /0.08] x (1.08)

= 3000(20.1153 - 1 /0.08] x (1.08)

= 3000 (19.1153/0.08) x (1.08)

= 3000 x 238.94 x 1.08

=774169.56 $

Thus At end of 64th birthday, she will have 774169.56$

Thus on 65th birthday her account balance will be

FV = PV(1+r)^n

=774169.56(1+8%)^1

=774169.56(1.08)

= 836103.12$

b) Here we need to find selling price per bond

Assuming face value to be 1000$

Interest = 1000 x 4% x 1/2 = 20$

n = 6 x 2 =12

YTM = 8%/2 = 4%

Price of bond = Interest x PVIFA(YTM%,n) + Redemtin value x PVIF(YTM%,n)

PVIFA(YTM%,n) = [1-(1/(1+r)^n)/r]

PVIFA(4%,12) = [1-1/(1+4%)^12 / 4%]

=[1-1/(1.04)^12 /0.04]

=[1-0.6246 / 0.04]

=0.3754/0.04

=9.38507

PVIF(YTM%,n) =1/(1+r)^n

PVIF(4%,12)=1/(1+4%)^12

=0.6246

Thus price of bond = 20 x 9.38507 + 1000 x 0.6246

= 187.70 + 624.597

=812.30$

Thus it will trade at 812.30/1000 x 100 = 81.23% of its issue price

Thus Garion will receive = 1,000,000 x 81.23% = 812300$

c) Here we need to find present value of intallments

=Installments x PVIFA(r%,n)

PVIFA(r%,n) = [1-(1/(1+r)^n)/r]

PVIFA(8%,6) = [1-(1/(1+8%)^6)/8%]

=[1-1/(1.08)^6 /0.08]

=[1-0.6302 / 0.08]

=0.3698/0.08

=4.6229

Thus PV of instalments

= 10000 x 4.6229

=46228.79$

PV of other option is $42000

Thus Installment option should be choosen

d) This can be solved using formula of FV(Annuity due)

FV(Annuity due) =A [(1+r)^n - 1/ r] x (1+r)

r= rate of interest = 8%

A = ?

n = 6

Thus 2,000,000 = A[(1+8%)^6 - 1 / 8%] x (1+8%)

2,000,000 = A[(1+0.08)^6 - 1 / 0.08] x (1+0.08)

2,000,000 = A[(1.08)^6 - 1 /0.08] x (1.08)

2,000,000 = A[1.58687-1 / 0.08] x 1.08

2,000,000 =A[0.58687/0.08] x 1.08

2,000,000 =A x 7.33593 x 1.08

2,000,000 =A x 7.92280

A = 252435.9 $