Question

Most of these problems will be easier using a spreadsheet.

1. What is the present value of a perpetuity with $5000 annual payments? Assume 3% discount rate.

2. How much money do you need to create an annuity of $2000/month for 20 years assuming you can invest the capital in an instrument (say treasuries) with a 3% rate and semi-annual compounding?

3. You wish to purchase a new car which costs $50,000. You have $10,000 for a down payment. The bank will charge you 8% (annual) and give you a 5-year loan (60 months). What is your monthly payment? Assume the interest is added at the end of each month.

4. Calculate the Payback, NPV, & IRR for the two projects.

a. For the Payback, assume first no discount rate and then discount the cash flows by 5%. How does the Discounted Payback period change?

b. For NPV, which project is best if the rate used is 10%? 15%?

c. What are the IRRs for each project?

year	Project1	Project 2
0	-15000	-18000
1	9500	10500
2	6000	7000
3	2400	6000

Answer 1

1

PV = annual payment/discount rate = 5000/0.03=166666.67

2

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+3/2*100)^2-1)*100

Effective Annual Rate% = 3.02

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 2000*((1-(1+ 3.0225/1200)^(-20*12))/(3.0225/1200))

PV = 359890.48

Please ask remaining parts separately, questions are unrelated. I have done one bonus