Question

1. You will receive $ 200 in a year. The applicable interest rate is 6%. The present value of this future income is

2. You have to pay $500.00 in 2 years and the interest rate is 5%. The present value of this payment is

3. A coupon bond with a face value of $ 8000 and $400 coupon payments every year has a coupon rate of ____ %.

4. If the amount payable in two years is $2420 for a simple loan at 10 percent interest, the loan

amount is $__________.

5. A security pays $55 in one year and $133.10 in three years. Present value of this security is $150. The relevant interest rate is ______%.

6. You buy a 5% coupon bond for $1000 and sell it for $1,200 after a year. Your rate of return is ______%.

7. If a security you can buy today for $200 pays $110 next year and $121 the year after that. Its yield to maturity is _________%.

8. If a perpetuity has a price of $500 and an annual interest payment of $25, the interest rate is ______%.

9. My annual electricity usage is 10,800 kWh. Ignoring seasonal variation let’s assume that the usage is 900 kWh per month. Each month, Duke Energy charges for my electricity usage as follows.

Fixed cost - $ 9

First 300 kWh - $ 0.13 per kWh

Next 600 kWh - $ 0.09 per kWh

I also pay a 7% tax on total bill.

My electricity usage is expected to stay at the same level for 30 years, but Duke is expected to raise charges by 2% each year.

Blue Raven Solar has proposed to fix 26 solar panels on my roof for a cost of $ 26,300. These panels can be used for 30 years. During the first year they produce 10,300 kWh and that drops by 0.5% each year due to system degradation.

I want your help to find my internal rate of return from this project if I go with this proposal.

My internal rate of return as a percentage is ________________

10. My annual electricity usage is 10,800 kWh. Ignoring seasonal variation let’s assume that the usage is 900 kWh per month. Each month, Duke Energy charges for my electricity usage as follows.

Fixed cost - $ 9

First 300 kWh - $ 0.13 per kWh

Next 600 kWh - $ 0.09 per kWh

I also pay a 7% tax on total bill.

My electricity usage is expected to stay at the same level for 30 years, but Duke is expected to raise charges by 2% each year.

Blue Raven Solar has proposed to fix 26 solar panels on my roof for a cost of $ 26,300. These panels can be used for 30 years. During the first year they produce 10,300 kWh and that drops by 0.5% each year due to system degradation.

This is what I already told you. But, I forgot to tell you one important thing.

There is a 26% Federal tax credit for going solar!

This means if I spend $ 26,300 in year 1, I will get 26% of that amount back in year 2 when I file my tax return.

I want your help to find my internal rate of return from this project considering this tax incentive too.

My internal rate of return as a percentage is ________________

Answer 1

Ans 1. Future amount = 200 $

interest rate = 6 %

Present value = Future amount / (1 + Rate of Interest)^1

= 200 / (1 + 6%)^1

= 200 / 1.06 = 188.67 $

Ans 2. Amount to be paid = 500 $

Time = 2 Years

Interest rate = 5 %

Present value = Future amount / (1 + Rate of Interest)^2

= 500 / (1 + 5%)^2

= 500 / (1.05)^2 = 500 / 1.1025 = 453.51 $

Ans3. Face Value of bond = 8000 $

Coupon Payment = 400 $

Current Yield = Coupon Payment / Face value of bond * 100

= 400 / 8000 * 100 = 5%

Ans4. Total Amount payable = 2420 $

Interest rate = 10 %

Time = 2 Years

Loan amont = Amount payable / (1 + interest rate)^n

= 2420 / (1 + 10%)^2

= 2420 / (1.10)^2

= 2420 / 1.21 = 2000 $

Therefore interest amount stands at 420 $ (2420 - 2000 )