Question

1. Suppose you want to buy some new furniture for your family room. You currently have $500 and the furniture you want costs $589. If you can earn 5%, how many years will you have to wait if you don’t add any additional money? Round your answer to two decimals.

2. How much would you need to invest at the end of each year if you need $40,000 in 9 years and you can earn 6% interest? Round your answer to two decimals.

3. You want to purchase a new pickup truck for $56526, and the finance office at the dealership has quoted you a 7% APR loan for 60 months to buy the truck.  What will your monthly payment be? Round your answer to two decimals.

4. You want to buy a new car for $32782.  The contract is in the form of a 60-month annuity due at a 4% APR.  What will your monthly payment be? Round your answer to two decimals.

5. Nittany Life Insurance Co. is offering to sell you an investment that will pay you and your heirs $3988 per year forever. If you require a 11% return on this investment, what is the most you should pay for this investment? Round your answer to two decimals.

6. You are evaluating this possible investment by using the IRR. If your required return is 18 percent, what is the IRR? Round your answer to two decimals.

           CASH FLOW

Year 1: -$130,000

Year 2: 68,000

Year 3: 71,000

Year 4: 54,000

7.

You are evaluating this possible investment by using the NPV. If your required return is 18 percent, what is the NPV? Should you go through with this investment? Round your answer to two decimals.

    CASH FLOW

Year 1: -$130,000

Year 2: 68,000

Year 3: 71,000

Year 4: 54,000

Answer 1

1)

Future value = Present value ( 1 + r)ⁿ

589 = 500 ( 1 + 0.05)ⁿ

1.178 = ( 1.05)ⁿ

LN 1.178 = n LN 1.05

0.163818 = n 0.04879

n = 3.36 years

It will take 3.36 years

2)

Future value of annuity = Annuity * [ ( 1 + r)ⁿ - 1] / r

40,000 = Annuity * [ ( 1 + 0.06)⁹ - 1] / 0.06

40,000 = Annuity * 11.491316

Annuity = $3,480.89

$3,480.89 needs to be invested at the end of each year

3)

rate = 0.07 / 12 = 0.005833

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r

56526 = Annuity * [ 1 - 1 / ( 1 + 0.005833)⁶⁰] / 0.005833

56526 = Annuity * 50.502475

Annuity = $1,119.27

Monthly payments will be $1,119.27

4)

Rate = 0.04 / 12 = 0.003333

Present value of annuity due = ( 1 + r) * Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r

32782 = ( 1 + 0.003333) * Annuity * [ 1 - 1 / ( 1 + 0.003333)⁶⁰] / 0.003333

32782 = ( 1.003333) * Annuity * 54.299601

Annuity = 601.72

Monthly payment will be $601.72

5)

Present value of perpetuity = Cash flow / interest rate

Present value of perpetuity =  3988 / 0.11

Present value of perpetuity = $36,254.55

6)

IRR is the rate of return that makes NPV equla to 0

NPV = -130,000 + 68,000 / ( 1 + R)¹ + 71,000 / ( 1 + R)² + 54,000 / ( 1 + R)³  

Using trial and error method i.e, after trying various values for R, let's try R as 23.65%

NPV = -130,000 + 68,000 / ( 1 + 0.2365)¹ + 71,000 / ( 1 + 0.2365)² + 54,000 / ( 1 + 0.2365)³

NPV = 0

Therefore IRR is 23.65%

7)

NPV = Present value of cash inflow - present value of cash outflows

NPV = -130,000 + 68,000 / ( 1 + 0.18)¹ + 71,000 / ( 1 + 0.18)² + 54,000 / ( 1 + 0.18)³  

NPV = $11,484.29