15. Bond ratings and prices A corporate bond with an 8.5 percent coupon has 10 years left to maturity. It has had a credit rating of A and a yield to maturity of 10 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BBB. The new appropriate discount rate will be 11.5 percent. What will be the change in the bond's price in dollars? Assume interest payments are paid semi-annually and par value is $1,000.
d = annual net patient revenue *(5 days/365)* interest rate% = ?
Annual bank fee = Bank fee *12 (months in the year since its annual fee) = ?
So, annual savings = Interest Earned – Annual bank fee = ?
2. St. Luke’s Convalescent Center has $200,000 in surplus funds that it wishes to invest in marketable securities. If transaction costs to buy and sell the securities are $2,200 and the securities will be held for three months, what required annual yield must be earned before the investment makes economic sense?
Surplus fund = $200,000
Transaction cost = $2,200
Holding period = 3 months
So, yield should be minimum $2,200.
Let minimum required annual yield = r%
Therefore, surplus fun *(3/12)*r% = minimum yield
3. Your firm is considering the following three alternative bank loans for $1,000,000: Assume that you would normally not carry any bank balance that would meet the 20 percent compensating balance requirement. What is the rate of annual interest on each loan?
a) 10 percent loan paid at year end with no compensating balance
Annual interest rate = 10%
b) 9 percent loan paid at year end with a 20 percent compensating ba
To calculate the change in the bond's price, we need to find the present value of the bond before and after the downgrade in credit rating and then subtract the two values.
Here's how you can calculate it step by step:
1. Determine the coupon payment per period:
The bond has an 8.5% coupon rate, which is paid semi-annually. Therefore, the coupon payment per period will be (8.5% / 2) * $1,000 = $42.50.
2. Determine the total number of periods:
Since the bond has 10 years left to maturity, and interest payments are made semi-annually, the total number of periods will be 10 * 2 = 20 periods.
3. Calculate the present value of the bond before the downgrade:
To find the present value, we'll discount the future cash flows (coupon payments and the final principal payment) at the yield to maturity rate of 10%.
a. Present value of coupon payments:
Using the present value of an ordinary annuity formula, the present value of the coupon payments before the downgrade can be calculated as follows:
PV_coupon = $42.50 * [(1 - (1 / (1 + (10% / 2))^20)) / (10% / 2)] = $666.04
b. Present value of principal payment:
The principal payment is the bond's par value of $1,000. Since the bond is redeemable at maturity, there is no discounting required for the principal payment.
c. Calculate the total present value before the downgrade:
Total PV_before = PV_coupon + Present value of principal payment = $666.04 + $1,000 = $1,666.04
4. Calculate the present value of the bond after the downgrade:
To find the present value after the downgrade, we'll discount the future cash flows at the new appropriate discount rate of 11.5%.
a. Present value of coupon payments:
Using the same formula as before, the present value of the coupon payments after the downgrade can be calculated as follows:
PV_coupon = $42.50 * [(1 - (1 / (1 + (11.5% / 2))^20)) / (11.5% / 2)] = $626.91
b. Present value of principal payment remains the same since it is not affected by the downgrade.
c. Calculate the total present value after the downgrade:
Total PV_after = PV_coupon + Present value of principal payment = $626.91 + $1,000 = $1,626.91
5. Calculate the change in the bond's price:
To find the change in the bond's price, subtract the total present value after the downgrade from the total present value before the downgrade:
Change in price = Total PV_before - Total PV_after = $1,666.04 - $1,626.91 = $39.13
Therefore, the change in the bond's price will be a decrease of $39.13.