Question

Annie Hegg has been considering investing in the bonds of Atilier Industries. The bonds were issued 5 years ago at their $1,000 par value and have exactly 25 years remaining until they mature. They have an 8% coupon interest rate, are convertible into 50 shares of common stock, and can be called any time at $1,080. The bond is rated Aa by Moody’s. Atilier Industries, a manufacturer of sporting goods, recently acquired a small athletic-wear company which was in financial distress. As a result of the acquisition, Moody’s and other rating agencies are considering a rating change for Atilier bonds. Recent economic data suggest that expected inflation, currently at 5% annually, is likely to increase to a 6% annual rate.

Annie remains interested in the Atilier bond but is concerned about inflation, a potential rating change, and maturity risk. To get a feel for the potential impact of these factors on the bond value, she decided to apply the valuation techniques she learned in her finance course.

To Do:

1. For each of the following required returns, calculate the bond’s value, assuming annual interest. Indicate whether the bond will sell at a discount, at a premium, or at par value.
   1. Required return is 6%.
   2. Required return is 8%.
   3. Required return is 10%.
2. Repeat the calculations in part
3. b, assuming that interest is paid semiannually and that the semiannual required returns are one-half of those shown. Compare and discuss differences between the bond values for each required return calculated here and in part b under the annual versus semiannual payment assumptions.
4. If Annie strongly believes that expected inflation will rise by 1% during the next few months, what is the most she should pay for the bond, assuming annual interest?
5. If the Atilier bonds are downrated by Moody’s from Aa to A, and if such a rating change will result in an increase in the required return from 8% to 8.75%, what impact will this have on the bond value, assuming annual interest?
6. After evaluating all of the issues raised above, what recommendation would you give Annie with regard to her proposed investment in the Atilier Industries bonds?

Answer 1

Since, there are multiple parts to the question. I have answered the first four (part b to part e)

______

Part b)

The bond's value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Required Return), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

_____

Bond Value when Required Return is 6%

Here, Rate = 6%, Nper = 25, PMT = 1,000*8% = $80 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(6%,25,80,1000) = $1,255.67

The bond will sell at premium when required return is 6%.

_____

Bond Value when Required Return is 8%

Here, Rate = 8%, Nper = 25, PMT = 1,000*8% = $80 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(8%,25,80,1000) = $1,000

The bond will sell at par when the required return is 8%.

_____

Bond Value when Required Return is 10%

Here, Rate = 10%, Nper = 25, PMT = 1,000*8% = $80 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(10%,25,80,1000) = $818.46

The bond will sell at discount when the required return is 10%.

_____

Part c)

The bond's value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Required Return), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

_____

Bond Value when Required Return is 6% and Interest is Paid Semi-Annually

Here, Rate = 6%/2 = 3%, Nper = 25*2 = 50, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(3%,50,40,1000) = $1,257.30

The bond will sell at premium when required return is 6%.

_____

Bond Value when Required Return is 8% and Interest is Paid Semi-Annually

Here, Rate = 8%/2 = 4%, Nper = 25*2 = 50, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(4%,50,40,1000) = $1,000

The bond will sell at par when required return is 8%.

_____

Bond Value when Required Return is 10% and Interest is Paid Semi-Annually

Here, Rate = 10%/2 = 5%, Nper = 25*2 = 50, PMT = 1,000*8%*1/2 = $40 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond's Value = PV(5%,50,40,1000) = $817.44

The bond will sell at discount when required return is 10%.

_____

Comparison

Required Return	Bond Value with Annual Interest Payment	Bond Value with Semi-Annual Interest Payment
6%	$1,255.67	$1,257.30
8%	$1000.00	$1000.00
10%	$818.46	$₹ 817.44

_____

Part d)

The bond's value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Required Return), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 8% + 1% = 9%, Nper = 25, PMT = 1,000*8% = $80 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Value (Amount Annie Should Pay) = PV(9%,25,80,1000) = $901.77

_____

Part e)

We will have to calculate revised bond's value at 8.75%.

The bond's value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for calculating PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Required Return), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 8.75%, Nper = 25, PMT = 1,000*8% = $80 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Value = PV(8.75%,25,80,1000) = $924.81

The bond value will decrease to $924.81 (at 8.75% required return) from $1,000 (at 8% required return)