Question

In: Finance

Allied Materials needs $8 Million in new capital for the expansion of its composites manufacturing facilities....

Allied Materials needs $8 Million in new capital for the expansion of its composites manufacturing facilities. It is offering a $10,000, 5% bond at a discount price of $8000. The bond matures in 20 years and pays a Semiannual dividend.

a) What is the effective annual rate of return to an investor who buys the bond?

b) What is the effective annual rate of return to an investor who buys the bond and then resales it to the second investor in six years (just after the 12th payment) for $8750?

c) What is the effective annual rate of return to the second investor?

Use financial excel functions =RATE & =EFFECT to help solve these questions.

Solutions

Expert Solution

a) What is the effective annual rate of return to an investor who buys the bond?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,000

M = value at maturity, or par value = $ 10,000

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 20 *2 = 40

YTM = interest rate, or yield to maturity =?

Now we have,

$8,000 = $250 * [1 – 1 / (1+YTM) ^40] /YTM + 10,000 / (1+YTM) ^40

From above equation, we can calculate the value of YTM, which is 3.43% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.43% = 6.85% per year

Effective annual rate = (1+3.43%) ^2 -1 = 6.97%

b) What is the effective annual rate of return to an investor who buys the bond and then resales it to the second investor in six years (just after the 12th payment) for $8750?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,000

M = value at maturity, or par value = $ 8,750

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 6 *2 = 12

YTM = interest rate, or yield to maturity =?

Now we have,

$8,000 = $250 * [1 – 1 / (1+YTM) ^12] /YTM + 8,750 / (1+YTM) ^12

From above equation, we can calculate the value of YTM, which is 3.76% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.76% = 7.52% per year

Effective annual rate = (1+3.76%) ^2 -1 = 7.66%

c) What is the effective annual rate of return to the second investor?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,750

M = value at maturity, or par value = $ 10,000

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 14 *2 = 28

YTM = interest rate, or yield to maturity =?

Now we have,

$8,750 = $250 * [1 – 1 / (1+YTM) ^28] /YTM + 10,000 / (1+YTM) ^28

From above equation, we can calculate the value of YTM, which is 3.18% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.18% = 6.36% per year

Effective annual rate = (1+3.18%) ^2 -1 = 6.46%

Calculation in excel:

a. b. c.
PV 8000 PV 8000 PV 8750
FV 10000 FV 8750 FV 10000
PMT 250 PMT 250 PMT 250
NPER 40 NPER 12 NPER 28
Rate (semiannual) 3.43% Rate (semiannual) 3.76% Rate (semiannual) 3.18%
Rate (annual) 6.85% Rate (annual) 7.52% Rate (annual) 6.36%
Rate (Effective) 6.97% Rate (Effective) 7.66% Rate (Effective) 6.46%


Related Solutions

The Scandrick Corporation needs to raise $65 million to finance its expansion into new markets. The...
The Scandrick Corporation needs to raise $65 million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. If the the offer price is $35 per share and the company’s underwriters charge a spread of 7 percent, how many shares need to be sold?
A company is hoping to expand its facilities but needs capital to do so. In an...
A company is hoping to expand its facilities but needs capital to do so. In an effort to position itself for expansion in 3 years, the company will direct half of its profits into investments in a continuous manner. The company's profits for the past 5 years are shown in the table. The company's current yearly profit is $1,160,000. (The current year corresponds to t = 0.) Profit over the Past Five Years Years Ago 5 4 3 2 1...
A company needs to borrow $10 million for its working capital needs. Its considering the following...
A company needs to borrow $10 million for its working capital needs. Its considering the following three alternatives: Forgo cash discounts granted with the credit terms of 3/10; net 30 Borrow from the bank at 15% requiring a compensating balances 12% Issue commercial paper with 180 day maturity, at 12%. Cost of placement will $100,000. Which alternative would be the best?
A company needs to borrow $10 million for its working capital needs. Its considering the following...
A company needs to borrow $10 million for its working capital needs. Its considering the following three alternatives: Forgo cash discounts granted with the credit terms of 3/10; net 30 Borrow from the bank at 15% requiring a compensating balances 12% Issue commercial paper with 180 day maturity, at 12%. Cost of placement will $100,000. Which alternative would be the best?
Fulton Corporation purchases new manufacturing facilities and assumes a 10 year mortgage of $7 million. The...
Fulton Corporation purchases new manufacturing facilities and assumes a 10 year mortgage of $7 million. The annual interest rate on the mortgage is 5.5% and payments are due at the end of each year.    a. Determine the mortgage payment that Fulton Corporation must make each year. Round to the nearest dollar. $Answer b. Use Excel to prepare a mortgage amortization schedule for the 10 years. To access an Excel template, click the following link: mortgage amortization schedule c. At...
Husker’s Tuxedo’s, Inc. needs to raise $262 million to finance its plan for nationwide expansion. In...
Husker’s Tuxedo’s, Inc. needs to raise $262 million to finance its plan for nationwide expansion. In discussions with its investment bank, Husker’s learns that the bankers recommend an offer price (or gross price) of $40 per share and they will charge an underwriter’s spread of $2.35 per share. Calculate the net proceeds per share to Husker’s from the sale of stock. How many shares of stock will Husker’s need to sell in order to receive the $262 million needed?
Gravity, Inc., needs to raise $46.5 million to fund its expansion plans. The company will sell...
Gravity, Inc., needs to raise $46.5 million to fund its expansion plans. The company will sell shares at a price of $27.70 in a general cash offer and the company's underwriters will charge a spread of 7 percent. How many shares need to be sold?
A farm is evaluating two options to expand its facilities to serve a new manufacturing plant....
A farm is evaluating two options to expand its facilities to serve a new manufacturing plant. The new plant will require 2000 telephone lines this year and another 2000 lines in 10 years. The plant will operate for 30 years. Option 1: Install now network with capacity to serve 4000 lines. This network will cost $27,000 and annual maintenance costs will be $1900. Option 2: Provide a network with capacity to serve 2000 lines now and a second network to...
The optical products division of Panasonic is planning a $3.5 million building expansion for manufacturing its...
The optical products division of Panasonic is planning a $3.5 million building expansion for manufacturing its powerful Lumix DMC digital zoom camera. If the company uses an interest rate of 16% per year, compounded monthly for all new investments, what is the uniform amount per quarter the company must make in order to recover its investment in 4 years?
Your firm needs $15 million of new manufacturing equipment. If purchased, the equipment will be depreciated...
Your firm needs $15 million of new manufacturing equipment. If purchased, the equipment will be depreciated straight-line over five years, after which you estimate you could sell the equipment for $1.25 million. In this case, you are also responsible for $1 million per year of maintenance costs. If leased, the annual lease payments will be $4.2 million per year for five years (beginning of year payments). Maintenance is included with the lease, but the lease does require a $0.5 million...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT