Question

A. A rational person would prefer which of the following cash flows.

a. $5,000 per year for 10 years with the first payment made one year from today

b. $5,000 per year for 10 years with the first payment made today

c. $50,000 paid today

d. $25,000 paid today and $25,000 paid next year

e. $49,000 paid today

B. What is the value today of a money machine that will pay $4,263.00 per year for 28.00 years? Assume the first payment is made one year from today and the interest rate is 15.00%.

C. What is the value today of a money machine that will pay $3,413.00 per year for 28.00 years? Assume the first payment is made 2.00 years from today and the interest rate is 15.00%.

D. What is the value today of a money machine that will pay $4,686.00 every six months for 14.00 years? Assume the first payment is made six months from today and the interest rate is 9.00%.

E. What is the value today of a money machine that will pay $3,787.00 every six months for 29.00 years? Assume the first payment is made 4.00 years from today and the interest rate is 12.00%.

Answer 1

A. Calculating the present value of the following cash flows, Assuming Interest rate/Discounting rate @ 10%

a). Present Value of $5,000 per year for 10 years with the first payment made one year from today:

  

5000 5000 15000 5000 (1+110)*(1+1002 *(1+110) *(1+1004 | 5000 5000 (1+1009 十 (1+110) 10

= $ 30722.84

b). Present Value of $5,000 per year for 10 years with the first payment made today:

Snon 5000 5000 5000 5000 15000 = 5000+ (1+10)*(1+ (10)? (1+ (10) *(1+ (10) ***(1+10)

= $ 33795.12

c). Present Value of $ 50000 today = $ 50000

d). Present Value of $25,000 paid today and $25,000 paid next year:

= 25000 - - 25000 (14.10)

= $ 47727.27

e) Present Value of  $49,000 paid today = $ 49000

So, a rational person should prefer to receive $ 50,000 today.

B). Present value of money machine that will pay $4263 for 28 years with the first payment is made one year from today:

Interest rate = 15%

4263 4263 4263 4263 (1+15)*(1+115)2 (1+15) 4263 4263 (14.1514 十 j+ + ; (1-15)27 十 (1+ 15) 28

= $ 27852.31

C). Present value of money machine that will pay $3413 for 28 years with the first payment is made 2 year from today:

Interest rate = 15%

3413 3413341334133413 11: (1+15)2 + (1+15)3 (1+15)4 (1+15)5 *: 3413 (1+ 15) 30 (1+115) 29 上

= $ 16860.90

D). Present value of money machine that will pay $4686 every six months for 14 years with the first payment is made six months from today:

Interest rate = 9%

Converting it into semiannually = 9% *6/12 : 4.5%

Converting time into semi annually = 14 years *2 : 28

PV

4686 468646864686 (14.045) (14.04512 (14.045) 4686 4686 (14.04514" (14.045)27 (1+2.045528

PV = $ 73771.10

Note- Since, I'm only allowed to answer maximum 4 sub-parts as per guidelines the same has been answered.