You are considering the purchase of an outstanding Nickel Corp bond that was issued at par on Oct. 2, 2007 with a 10-year maturity. It is now Oct 2, 2013. The bond has an 8% coupon rate and has semi-annual coupons. The price is now $1,068.23.

a) If you bought this bond today and held it to maturity, what would be the return on this bond? State your return as an annual rate, which is calculated as two times the six month rate.

b) Next year the YTM on this bond decreases by 1 percentage point on an annual basis and you decide to sell it. What percentage will your bond sell for?

c) Re: b) what was your rate of return for this investment?

To calculate the return on the bond, we need to consider the bond's coupon payments, its purchase price, and its maturity value.

a) First, let's calculate the annual coupon payment. The bond has an 8% coupon rate, which means it pays 8% of its face value as interest every year. Since this bond has a face value of $1,000 (issued at par), the annual coupon payment is 8% * $1,000 = $80.

Since the bond pays coupons semi-annually, we need to calculate the number of coupon periods remaining until maturity. The bond has a maturity of 10 years, which means it has 10 * 2 = 20 six-month periods remaining.

Now, let's calculate the total coupon payments until maturity. There are 20 six-month periods remaining, so the total coupon payments will be 20 * $80 = $1,600.

The purchase price of the bond is $1,068.23. At maturity, the bond will be redeemed at its face value of $1,000.

To calculate the return, we need to add the total coupon payments to the difference between the face value and purchase price, and then divide by the purchase price.

Return = (Total Coupon Payments + (Face Value - Purchase Price)) / Purchase Price

Return = ($1,600 + ($1,000 - $1,068.23)) / $1,068.23

Calculating this expression gives a return of approximately 4.88%.

Since we want to express the return as an annual rate, we multiply the return by 2.

Annual return = 4.88% * 2 = 9.76%

So, if you bought this bond today and held it to maturity, the annual return on this bond would be approximately 9.76%.

b) Next year, if the Yield to Maturity (YTM) on the bond decreases by 1 percentage point, it means the interest rates have dropped. When interest rates drop, bond prices tend to increase.

To calculate the new price at which the bond will sell, we can use the bond pricing formula. The formula is:

Bond Price = (Coupon Payment / (1 + YTM/2)^n) + (Face Value / (1 + YTM/2)^n)

Where:
Coupon Payment = $80 (annual coupon payment / 2)
YTM = (Previous YTM - 1%) = (8% - 1%) = 7%
n = Remaining six-month periods until maturity (19 periods)

Plugging in these values into the formula:

Bond Price = ($80 / (1 + 7%/2)^19) + ($1,000 / (1 + 7%/2)^19)

Calculating this expression gives a bond price of approximately $1,113.99.

Therefore, if you decide to sell the bond next year when the YTM decreases by 1 percentage point, it will sell for approximately $1,113.99.

c) To calculate the rate of return for this investment, we need to consider the purchase price, the selling price, and the holding period. We'll assume the holding period is one year. The rate of return can be calculated using the following formula:

Rate of Return = (Selling Price - Purchase Price) / Purchase Price

Rate of Return = ($1,113.99 - $1,068.23) / $1,068.23

Calculating this expression gives a rate of return of approximately 4.28%.

So, the rate of return for this investment would be approximately 4.28%.