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Probationary period at the Cosmo K Manufacturing Group continues

Your probationary period at the Cosmo K Manufacturing Group continues. Your supervisor, Gerry, assigns you a project each week to test your competence in finance. This week, Gerry has asked you to evaluate several investment opportunities available to the company. Your instructions are to consider each situation independently of the others, unless otherwise indicated.

Evaluating Investment Opportunities
Consider the following situations and answer the related questions:

Your company has the opportunity to make an investment that promises to pay $24,000 after 6 years. If your company has a required return of 8.5% on this type of investment, what is the maximum amount that the company should pay for the investment? Explain your answer.
In the previous scenario, assume that your company negotiated a deal where it would pay $12,000 for the investment and receive a payment of $24,000 at the end of 7 years. What is the IRR on this investment? Should the company make the investment? Explain your answer.
Another investment opportunity available to your company involves the purchase of some common stock from Zorp Corporation. The company has asked you to evaluate the stock, which paid a dividend of $4.25 last year and is currently selling for $36 per share. If your company decides to buy the stock, the stock will be held for 5 years and then sold. The growth rate on the stock is constant at 3% per year, and your company's required return on the stock would be 11%. What is the maximum price per share that your company should pay for the stock?
Zorp Corporation also has some bonds for sale that your company is considering. These bonds have a $1,000 par value and will mature in 16 years. The coupon rate on the bonds is 5% paid annually, and they are currently selling for $987 each. The bonds are call protected for the next 4 years, and after this period, they are callable at 105. On the basis of this information, answer the following questions:
What is the YTM on these bonds?
If the bonds are called immediately after the call protection period, what would be the yield to call (YTC)?
If the bonds paid interest semiannually instead of annually, would the YTC, the YTM, or both change? Explain your answers.

Full Answer Section

Plugging in the values:

$P V = ( 1 + 0.085 ) ^{6} 24 , 000$ $P V = ( 1.085 ) ^{6} 24 , 000$ $P V = 1.65376 24 , 000$ $P V \approx 14, 512.87$

Explanation:

The maximum amount the company should pay for this investment is approximately $14,512.87. This is because, at a required rate of return of 8.5%, an investment of this amount today would grow to $24,000 after 6 years. Paying any more than this would result in a return lower than the company's required 8.5%, making the investment less attractive.

2. Internal Rate of Return (IRR) and Investment Decision

In this scenario, the company pays $12,000 for an investment that returns $24,000 after 7 years. To find the Internal Rate of Return (IRR), we need to determine the discount rate that makes the net present value (NPV) of the investment equal to zero.

The equation to solve for IRR in this case is:

$0 = - I ni t ia l I n v es t m e n t + ( 1 + I RR ) ^{n} F u t u re Va l u e$ $0 = - 12, 000 + ( 1 + I RR ) ^{7} 24 , 000$

We can solve for IRR by rearranging the equation:

$( 1 + I RR ) ^{7} 24 , 000 = 12, 000$ $(1 + I RR)^{7} = 12 , 000 24 , 000$ $(1 + I RR)^{7} = 2$ $1 + I RR = 2^{1/7}$ $1 + I RR \approx 1.10409$ $I RR \approx 0.10409$ or $10.41%$

Should the company make the investment?

Yes, the company should likely make the investment. The calculated Internal Rate of Return (IRR) of approximately 10.41% is higher than the company's required rate of return of 8.5%. An IRR greater than the required return generally indicates that the investment is expected to be profitable and create value for the company.

3. Maximum Price per Share for Zorp Corporation Stock

To determine the maximum price per share the company should pay for Zorp Corporation stock, we can use the Dividend Discount Model (DDM) for a stock that will be held for a specific period and then sold. Since we have a holding period and a future sale, we need to consider both the present value of the dividends received during the holding period and the present value of the expected selling price.

First, let's calculate the expected dividends over the next 5 years:

$D_{0}$ (Last year's dividend) = $4.25
Growth rate ( $g$ ) = 3% or 0.03

$D_1 = D_0 \times (1 + g) = 4.25 \times (1.03) = $4.38$ $D_2 = D_1 \times (1 + g) = 4.38 \times (1.03) = $4.51$ $D_3 = D_2 \times (1 + g) = 4.51 \times (1.03) = $4.65$ $D_4 = D_3 \times (1 + g) = 4.65 \times (1.03) = $4.79$ $D_5 = D_4 \times (1 + g) = 4.79 \times (1.03) = $4.93$

Next, we need to estimate the selling price of the stock at the end of year 5. We can use the Gordon Growth Model to estimate the future price at year 5 ( $P_{5}$ ), assuming the dividend in year 6 ( $D_{6}$ ) will continue to grow at 3%:

$P_{5} = ( r - g ) D ^{6}$

Where:

$r$ = Required return (11% or 0.11)
$D_6 = D_5 \times (1 + g) = 4.93 \times (1.03) = $5.08$

$P_{5} = ( 0.11 - 0.03 ) 5.08$ $P_{5} = 0.08 5.08$ $P_5 = $63.50$

Now, we need to calculate the present value of all the expected cash flows (dividends and the selling price) discounted at the company's required return of 11%:

$P V = ( 1 + r ) ^{1} D ^{1} + ( 1 + r ) ^{2} D ^{2} + ( 1 + r ) ^{3} D ^{3} + ( 1 + r ) ^{4} D ^{4} + ( 1 + r ) ^{5} D ^{5} + P ^{5}$

$P V = ( 1.11 ) ^{1} 4.38 + ( 1.11 ) ^{2} 4.51 + ( 1.11 ) ^{3} 4.65 + ( 1.11 ) ^{4} 4.79 + ( 1.11 ) ^{5} 4.93 + 63.50$

$P V = 1.11 4.38 + 1.2321 4.51 + 1.367631 4.65 + 1.518070 4.79 + 1.685058 68.43$

$P V \approx 3.95 + 3.66 + 3.40 + 3.15 + 40.61$ $P V \approx 54.77$

The maximum price per share that the company should pay for the stock is approximately $54.77.

4. Zorp Corporation Bonds

a) Yield to Maturity (YTM)

To calculate the Yield to Maturity (YTM), we need to find the discount rate that equates the present value of the bond's future cash flows (coupon payments and par value) to its current market price.

Given:

Par Value (FV) = $1,000
Coupon Rate = 5% (annual payment of $0.05 \times 1000 = $50)
Years to Maturity (n) = 16
Current Selling Price (PV) = $987

We need to solve for 'r' in the following equation:

$P V = ( 1 + r ) ^{1} PMT + ( 1 + r ) ^{2} PMT + ... + ( 1 + r ) ^{n} PMT + F V$

$987 = ( 1 + r ) ^{1} 50 + ( 1 + r ) ^{2} 50 + ... + ( 1 + r ) ^{16} 50 + 1000$

Solving this equation for 'r' typically requires an iterative process or the use of a financial calculator or spreadsheet software. Using a financial calculator or spreadsheet function, the approximate YTM is 5.11%.

b) Yield to Call (YTC)

To calculate the Yield to Call (YTC), we need to find the discount rate that equates the present value of the cash flows until the call date (including the call price) to the current market price.

Given:

Current Selling Price (PV) = $987
Annual Coupon Payment (PMT) = $50
Years to Call Protection = 4 years
Call Price = 105% of par value = $1,000 \times 1.05 = $1,050
Number of periods until call (n) = 4

We need to solve for 'r' in the following equation:

$P V = ( 1 + r ) ^{1} PMT + ( 1 + r ) ^{2} PMT + ( 1 + r ) ^{3} PMT + ( 1 + r ) ^{4} PMT + C a llP r i ce$

$987 = ( 1 + r ) ^{1} 50 + ( 1 + r ) ^{2} 50 + ( 1 + r ) ^{3} 50 + ( 1 + r ) ^{4} 50 + 1050$

$987 = ( 1 + r ) ^{1} 50 + ( 1 + r ) ^{2} 50 + ( 1 + r ) ^{3} 50 + ( 1 + r ) ^{4} 1100$

Using a financial calculator or spreadsheet software, the approximate YTC is 6.54%.

c) Impact of Semiannual Interest Payments

If the bonds paid interest semiannually instead of annually, both the YTC and the YTM would change. Here's why:

Number of Periods: The number of periods would double. For YTM, it would become 16 years * 2 = 32 periods. For YTC, it would become 4 years * 2 = 8 periods.
Periodic Interest Payment: The semiannual interest payment would be half of the annual payment, so $50 / 2 = $25 per period.
Discount Rate per Period: The discount rate (YTM or YTC) would be expressed as a rate per half-year period. To get the annualized yield, this periodic rate would typically be multiplied by 2.

Specifically:

YTM would change: With semiannual compounding, the total return over the life of the bond would be calculated differently, leading to a different annualized yield that equates the present value of the semiannual cash flows to the current price.
YTC would change: Similarly, the calculation for YTC would involve discounting semiannual coupon payments and the call price over the 8 semiannual periods until the call date, resulting in a different annualized yield to the call.

In general, for bonds selling at a discount (like these), the semiannual YTM will be slightly higher than the annual YTM because the interest is compounded more frequently. The same principle applies to the YTC.

Sample Answer

Maximum Investment Amount for a Future Payment

To determine the maximum amount the company should pay for an investment that promises $24,000 after 6 years, given a required return of 8.5%, we need to calculate the present value of that future payment.

The formula for present value (PV) is:

$P V = ( 1 + r ) ^{n} F V$