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Bonds and Leasing
Q1
(R company) bonds trade at 100 today. The bonds pay semiannual interest thatis paid on January 1 and july 1 . the coupon on the bond is 10 percent. How much will you pay for a )r) bond if today is
a. March 1.
b. October 1
c. July 1
d. August 15
Q2
(B company) intend to issue callable, perpetual bonds. The bonds are Callable at \$1,250. One-year interest rates are 12 percent. There is a 6-percent probability that long-term interest rates are 12 percent. There is a 60% probability that long-term interest rates one year from today will be 15%. With a 40%, probability lng term interest rate will be 8%. To simplify the firms accounting (B) would like to issue the bonds at par (\$1,000.). What must the coupon on the bonds be for the (B) to be able to be able to sell them at par?
Q3
The CFO of CRA is considering whether or not to refinance the two currently outstanding corporate bonds of the firm. The first one is an 8% perpetual bond with a \$1000 face value with \$75 million outstanding. The second one is a 9% perpetual bond with the same face value with \$87.5 million outstanding . the call premiums for the two bonds are 8.5% and 9.5% of the face value , respectively. The transaction costs of the refunding are \$10 million and \$12 million. Respectively. The current interest rate for the two bonds are 7% and 7.25% respectively . which bond should the CFO recommend be refinanced ? what is the NPV of the refunding ?
Q4
SSE firm is considering borrowing money at 11% and purchasing a machine that costs \$350,000. The machine will be depreciated over 5 years by the streightline method and will be worthless in 5 years. SSE can lease the machine with the year-end payment of \$94,200. The corporate tax rate is 35%. Should SSEbuy or lease?
Q5
RRC wants to expand its manufacturing facilities. LLC has offered RRC the opportunity to lease a machine for \$100,000 for 5 years. The machine will be fully6 depreciated by the straight-line method. The corp. tax rate for RRc is 25%. While LLC tax rate is 35%. The appropriate before-tax interest rate is 8%. Assume lease payments occur at year end. What is RRC reservation price? What is LLC's reservation price? What is the negotiating range of the lease?

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Bonds and Leasing
Q1
(R company) bonds trade at 100 today. The bonds pay semiannual interest thatis paid on January 1 and july 1 . the coupon on the bond is 10 percent. How much will you pay for a )r) bond if today is
a. March 1.
b. October 1
c. July 1
d. August 15
a. If you purchase the bond on March 1, you owe the seller two months of interest. The seller owned the bond for two months since the last interest payment date (January 1).
The interest rate on the bond is 10%. The interest per month is 0.8333% (=10% / 12). 1.6667% (= 0.8333% x 2) is the interest for two months. The interest amount is 1,000X1.6667%=16.67. The total amount to be paid is the face value + the accrued interest = 1,000+16.67 = 1,016.67
b. If you purchase the bond on October 1, you owe the seller three months of interest. The seller owned the bond for three months since the last interest payment date (July 1).
The interest rate on the bond is 10%. The interest per month is 0.8333% (= 10% / 12). 2.5% (0.8333% x 3) is the interest for three months. The interest amount is 1,000X2.5%=\$25. The total amount to be paid is the face value + the accrued interest = 1,000+25 = \$1,025
c. Since July 1 is an interest payment date, there is no accrued interest on the bonds. If today is July 1, you will pay 100% of the face value for the bond. If the face value of the bonds is \$1,000, then you will pay \$1,000.
d. If you purchase the bond on August 15, you owe the seller six weeks of interest. The seller owned the bond for six weeks since the last interest payment date (July 1). The interest rate on the bond is 10%. The interest per two week period is 0.41667% (10% / 24). 1.25% (=0.41667% x 3) is the interest six weeks. The interest amount is 1,000X1.25%=12.50. The total amount to be paid is the face value + the accrued interest = 1,000+12.50 = \$1,012.50
Q2
(B company) intend to issue callable, perpetual bonds. The bonds are Callable at \$1,250. One-year interest rates are 12 percent. There is a 60% probability that long-term interest rates one year from today will be 15%. With a 40%, probability lng term interest rate will be 8%. To simplify the firms accounting (B) would like to issue the bonds at par (\$1,000.). What must the coupon on the bonds be for the (B) to be able to be able to sell them at par?
If interest rates rise to 15%, the price of the bonds will fall. If the price of the firm's bonds is low, B company will not call them. In this case, the bondholders will receive the coupon payment, C. They will still be holding a bond worth C/0.15 (the bond is a perpetual bond and so the value is given as Coupon Payment/Interest rate) . Their total holding will be C + C / 0.15 ( the interest amount + the value of the bond).
If interest rates fall to 8%, it is highly likely that the price of the bonds will rise above the call price. If this happens, B Company will call the bonds. In this case, the bondholders will receive the call price, \$1,250, plus the coupon payment, C.
The selling price today of the bonds is the PV of the expected payoffs to the bondholders. The expected payoff is 0.6 (C + C / 0.15) + 0.4 (C + \$1,250). Since B Company wants today's price of the bonds to be \$1,000 ( the company wants to sell the bonds at par), discount the expected payoffs at the current rate of interest and solve for C.
\$1,000 = [0.6 (C + C/0.15) + 0.4 (C + \$1,250)] / 1.12 ( the rate for 1 year is 12%)
C = \$124.00
The coupon payment for the year must be \$124.00. Thus, the coupon rate which ensures that the bonds will sell at par is 12.4 % (=\$124.00 / \$1,000).
Q3
The CFO of CRA is considering whether or not to refinance the two currently outstanding corporate bonds of the firm. The first one is an 8% perpetual bond with a \$1000 face value with \$75 million outstanding. The second one is a 9% perpetual bond with the same face value with \$87.5 million outstanding . the call premiums for the two bonds are 8.5% and 9.5% of the face value , respectively. The transaction costs of the refunding are \$10 million and \$12 million. Respectively. The current interest rate for the two bonds are 7% and 7.25% respectively . which bond should the CFO recommend be refinanced ? what is the NPV of the refunding ?
Bond 1
Coupon rate 8%
Current rate 7%
Face value \$1,000
Outstanding \$75,000,000
Refunding costs \$10,000,000

Bond 2
Coupon rate 9%
Current rate 7.25%
Face value \$1,000
Outstanding \$87,500,000
Refunding costs \$12,000,000
We find the NPV of the 2 bonds to decide.
For Bond 1, the savings in interest is 1% or 750,000 per year. The present value is 750,000/7%=10,714,285 ( the bonds are perpetual and so the PV is amount/discounting rate). The costs are 10,000,000 and call premium of 6,375,000.
The NPV is Savings - Cost = 10,714,285 - (10,000,000+6,375,000) = -5,660,715
For Bond 2, the savings in interest is 1.75% or 1,531,250. The PV is 1,531,250/7.25%=21,120,689. The costs are 12,000,000 and call premium of 8,312,500. The NPV is 21,120,689-12,000,000-8,312,500 = \$808,189
Bond 2 should be refinanced as it has a positive NPV.

Q4
SSE firm is considering borrowing money at 11% and purchasing a machine that costs \$350,000. The machine will be depreciated over 5 years by the streightline method and will be worthless in 5 years. SSE can lease the machine with the year-end payment of \$94,200. The corporate tax rate is 35%. Should SSEbuy or lease?
First, find the deprecation benefit (depreciation tax shield in case of purchase). This will be lost of the machine is leased.
Straight line depreciation = 350,000/5 = 70,000
Depreciation tax shield = 70,000X0.35 = 24,500
Second, find after tax discount rate
= .11 ( 1-.35)
= .0715

We now put together for the incremental cash flows from leasing instead of purchasing:

Lease minus Buy Year 0 Year 1 - 5
Lease
Lease payment -\$94,200
Tax benefit of lease payment (Amount x tax rate) \$32,970

Cost of machine -\$350,000
Depreciation Tax shield (lost in case of lease and so is subtracted) -\$24,500
Lease - Buy \$350,000 -\$85,730

Now find the NPV to make the lease/buy decision.
NPV = \$350,000 - \$85,730 X PVIFA (5, 7.15%)
= -\$102.66 < \$0
Since the NPV of leasing rather than buying is negative, the firm should buy the machine.

Q5
RRC wants to expand its manufacturing facilities. LLC has offered RRC the opportunity to lease a machine for \$100,000 for 5 years. The machine will be fully6 depreciated by the straight-line method. The corp. tax rate for RRc is 25%. While LLC tax rate is 35%. The appropriate before-tax interest rate is 8%. Assume lease payments occur at year end. What is RRC reservation price? What is LLC's reservation price? What is the negotiating range of the lease?
The reservation price is the least amount that would be acceptable as lease payments. It is calculated by setting the NPV of the cash flows = 0.
NPV = Cost - PV of lease payments, setting NPV=0 we get
0 = Cost - PV of lease payments
a. RRC
The cash flows for RRC are
The cost of the machine is \$100,000. Let L be the lease payments to be made. There will be tax benefit, so we consider the after tax payments. The after tax lease payment is L X (1-0.25) = 0.75L
The discounting rate is the after tax rate = 8% X (1-0.25) = 6%.
Since the lease payments are an annuity, the PV for 5 years and 6% is
0.75L X PVIFA (5,6%) = 0.75L X 4.21236 ( this factor from the PVIFA table)
We get 0 = 100,000-0.75LX4.21236
This gives L as \$31,652.85
This is the reservation price for RRC
b) LLC
Doing in the same way
The cash flows for LLC are
The cost of the machine = \$100,000
The lease income which we have to find is say L.
Since LLC owns the equipment, it will get the depreciation expense and so the depreciation tax shield. The depreciation per year is 100,000/5=20,000. The depreciation tax shield is 20,000X0.35=7,000
The after tax discounting rate is 8% X (1-0.35)=5.2%
We get
NPV= Cost - PV of Income from lease - PV of depreciation tax shield
0 = 100,000- L X (1-0.35) X PVIFA (5,5.2%)- 7,000 X PVIFA (5,5.2%)
0 = 100,000 - 0.65L X 4.3056 - 7,000X 4.3056
This gives
L = 69,860.8/2.79864 = \$24,962.04
This is the reservation price for LLC
The negotiation range is between \$24,962.04 ( which is the minimum acceptable to LLC) and \$31,652.85 ( which is the maximum that will be paid by RRC).

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