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Bonds, Investment Decision Rules, Capital Budgeting

3. KC Kincaid just purchased a U.S. Government bond with a 7.5 percent coupon rate and 15 years to maturity. The bond is currently priced to yield 5 percent (i.e., the current price reflects a semiannually compounded yield to maturity of 5 percent). Assuming that all future coupon payments will be reinvested at 6 percent compounded semiannually (due to a sudden increase in interest rates immediately following KC's purchase of the bond), determine the reinvested rate of return (i.e., the modified internal rate of return) from holding this bond to its maturity in 15 years.

4. Due to OGN Corporation's recent failure to obtain FDA approval for Graftskin, a medical technology to be used in the treatment of burn victims, security analysts believe that there is a 6 percent probability that the firm will default on its outstanding bonds. OGN's bonds have an annual coupon rate of 8 percent (with a single interest payment at the end of each year) and mature in exactly one year. The yield to maturity for risk-free bonds with one year to maturity is 5 percent. Assuming that investors value risky bonds by discounting the expected payoffs at the risk-free rate plus a risk premium of 1.5 percent to compensate for the risk of default,

a. Determine the promised yield to maturity for the OGN's 8 percent bonds
b. Determine the expected rate of return on OGN's 8 percent bonds.

7. Judy Johnson has just purchased a new home for $100,000. Judy is being allowed to borrow the full $100,000 purchase price of the home from Skiatook Federal Savings (SFS) under a new loan program designed for upwardly mobile professionals. The mortgage loan offered by the bank has an interest rate of 6 percent compounded monthly. However, although the loan is scheduled to be repaid monthly over a period of thirty years, the terms of the loan are unique in that Judy will be require to pay only $250 per month during the first four years of the loan term. During this time (the first four years), any differential between Judy's monthly payment and the monthly interest that accrues on the outstanding balance of the loan (at a yearly rate of 6 percent) will be added on to Judy's outstanding loan balance. SFS refers to this loan program as a graduated-balance mortgage because Judy will "graduate" to owing the bank more money
at the end of four years. Assuming that Judy makes her monthly payments of $250 per month as scheduled during the first four years of the loan term, determine

a. the outstanding balance on Judy's loan at the end of four years
b. the monthly payment that will be required on the loan at the end of four years

12. The portfolio managers who manage the assets of university endowment funds are usually compensated with a yearly fee that is set to equal a fixed proportion of the dollar value of the assets under management. Assume you are managing a large portfolio of stocks for the athletic department of a prestigious university. The endowment portfolio has a current dividend yield of 3.5 percent (expected date 1 dividend divided by today's market price). The dividends on the portfolio are paid out each year to fund the athletic scholarships provided by the university. The expected dividends and the portfolio value are both expected to grow forever at the same constant rate. Your annual fee for managing the portfolio is 0.6 percent (i.e., 0.006) to be paid at the end of the year based on the end of the year portfolio value. The portfolio is expected to have a total value of $70 million at the end of this year. Assuming that you have an ironclad contract to manage the portfolio from now to eternity (forever), determine the present value of the management contract.

14. Bradley Corporation is a diversified manufacturer of recreational products. The firm has begun to specialize in products that utilize the nanotechnology being developed at the University of Texas at Dallas. The firm's Chief Financial Officer (CFO) has just presented a proposal to sell the firm's boat manufacturing division, whose products all utilize outdated fiberglass construction. An anonymous buyer has offered (through a business broker) to purchase the boat division from Bradley for a price equal to the division's book value of $40 million (i.e., there is no capital gain on the sale so the after-tax proceeds from the sale would be $40 million). Boat sales in the upcoming fiscal year are expected to be $48 million. Yearly sales have been declining in the face of strong competition from manufacturing firms located in Paraguay. The CFO believes that the trend in boat sales cannot be reversed, and that sales from the boat division will continue to decline over the next 10 years at a rate of 8.0 percent per year. At the end of 10 years, the boat plant will have to be closed due to the imposition of costly OSHA regulations pertaining to the use of fiberglass in boat production. The CFO estimates that Webb's profit margin on boat sales is 25 percent, but has argued that selling the boat division is attractive because the proposed sale offers Webb a strong internal rate of return. Assuming that
Webb has a marginal tax rate of 30 percent,
a. Compute the internal rate of return for the incremental cash flows from selling the boat division
b. Discuss the conditions under which Webb should agree to the sale.

15. Symbiotic Ecosystems Incorporated (SEI) has hired you as a consultant to assess the economic feasibility of investing $500,000 to purchase a fully operational toad ranch. The ranch is currently capable of raising and bringing to market 1,000,000 toads per year. The toads can currently be sold as environmentally safe insect control mechanisms for $200 per 1000 (toads). Due to a world-wide shortage of toads and increasing concern over the environmental damage caused by pesticides, the price of toads is expected to increase at 10 percent per year for centuries to come. The cost of labor, which will be $150,000 next year, is expected to continue to increase in perpetuity at a rate of 5 percent per year. The apparatus used to aerate (supply oxygen to) the lagoon in which the toads reside is currently badly in need of replacement. The current cost to replace the aerator is $100,000. Although aerators do not qualify for any investment tax credit, the aerator can be depreciated to a zero salvage value over a four-year period using straight-line depreciation. An industrial engineer hired by SEI estimates that the aerator will have to be replaced every five years. The cost of aerators is expected to increase at 6 percent per year far into the foreseeable future. Assuming that Symbiotic Ecosystems has an opportunity cost of capital of 15 percent and a corporate tax rate of 40 percent, determine whether Symbiotic Ecosystems should acquire the toad ranch.

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3. KC Kincaid just purchased a U.S. Government bond with a 7.5 percent coupon rate and 15 years to maturity. The bond is currently priced to yield 5 percent (i.e., the current price reflects a semiannually compounded yield to maturity of 5 percent). Assuming that all future coupon payments will be reinvested at 6 percent compounded semiannually (due to a sudden increase in interest rates immediately following KC's purchase of the bond), determine the reinvested rate of return (i.e., the modified internal rate of return) from holding this bond to its maturity in 15 years.

First, we need to calculate how much the bonds have been issued, which is told by the yield to maturity of 5%, by using the formula as follows: -

where B is the issued price
C is the coupon payment
r is the discount or yield rate
n is the period

Then, we can replace the information into the equation. Coupon payment is equal to $1,000 x 7.5% = 75, semiannual coupon = 37.50)

The issued price of the bond is equal to

B = 37.50 x [1 - 1 ] + 1,000
(1.025)30 (1.025)30
0.025

B = 37.50 x 20.9306 + 1,000/2.0976
B = $1,261.63

The modified IRR assumes that all cash flows are reinvested at 6% compounded semiannually for the next 15 years. Then, we will find how much MIRR by using FVA to find the future value of the coupon payment reinvested. Then, we will find the present value of terminal value must be equal to the cash outflow.

We have to use annuity formula to solve the problem.

FVA = W x (1 + i)n - 1 where FVA is the future value
i W is the amount required to invest at the end of each year
i is the interest rate
n is the period

FVA = 37.50 x (1 + 0.03)30 - 1
0.03

FVA = 37.50 x 40.568
FVA = $1,521.30

Terminal value = $1,521.30 + $1,000 = $2,521.30

PV = FV/(1 + MIRR)n where PV is the present value
FV is the terminal value
MIRR is the interest rate
n is the period
1,261.63 = 2,521.30/(1 + MIRR)30
(1 + MIRR)30 = 1.9984
1 + MIRR = (1.9984)(1/30)
1 + MIRR = 3.3347
MIRR = 2.3347% semiannually or 4.6694% per year

4. Due to OGN Corporation's recent failure to obtain FDA approval for Graftskin, a medical technology to be used in the treatment of burn victims, security analysts believe that there is a 6 percent probability that the firm will default on its outstanding bonds. OGN's bonds have an annual coupon rate of 8 percent (with a single interest payment at the end of each year) and mature in exactly one year. The yield to maturity for risk-free bonds with one year to maturity is 5 percent. Assuming that investors value risky bonds by discounting the expected payoffs at the risk-free rate plus a risk premium of 1.5 percent to compensate for the risk of default,

a. Determine the promised yield to maturity for the OGN's 8 percent bonds

First we need to find the price of OGN's bond.

Since the risk-free bonds with one year to maturity is 5 percent. Assuming that investors value risky bonds by discounting the expected payoffs at the risk-free rate plus a risk premium of 1.5 percent to compensate for the risk of default, the market rate will be equal to 6.5%.

a. We need to calculate how much the bonds have been issued by using the formula as follows: -

where B is the issued price
C is the coupon payment
r is the discount rate
n is the period

C, which is the annual coupon payment, can be calculated by multiplying $1,000 with 8%. We will get ...

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