Your 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.

Sample Solution

Situation 1: Single Future Payment

Question: What is the maximum amount that the company should pay for the investment that promises to pay $24,000 after 6 years, given a required return of 8.5%? Explain your answer.
Answer: The maximum amount the company should pay for this investment is the present value of the future payment, discounted at the company's required rate of return.

We can calculate the present value (PV) using the following formula:

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

Full Answer Section

Where:
- FV = Future Value = $24,000
- r = Required Rate of Return = 8.5% or 0.085
- n = Number of Years = 6
Plugging in the values:

$P V = ( 1 + 0.085 ) ^{6} $24 , 000$ $P V = ( 1.085 ) ^{6} $24 , 000$ $P V = 1.65375 $24 , 000$ $P V \approx $14, 512.76$

Explanation: The present value represents the amount of money the company would need to invest today at an 8.5% return to have $24,000 in 6 years. Therefore, the company should not pay more than approximately $14,512.76 for this investment to achieve its required rate of return. Paying any more would result in a return lower than 8.5%.

Situation 2: Negotiated Deal - IRR Analysis

Question: Assume the company pays $12,000 for the investment and receives $24,000 at the end of 7 years. What is the IRR on this investment? Should the company make the investment? Explain your answer.
Answer: To find the Internal Rate of Return (IRR), we need to find the discount rate that makes the net present value (NPV) of the investment equal to zero. In this simple case with a single outflow and a single inflow, we are solving for 'r' in the following equation:

$0 = - $12, 000 + ( 1 + r ) ^{7} $24 , 000$

We can rearrange this to solve for $(1 + r)^{7}$ :

$(1 + r)^{7} = $12 , 000 $24 , 000$ $(1 + r)^{7} = 2$

Now, we take the 7th root of 2:

$1 + r = (2)^{1/7}$ $1 + r \approx 1.10409$ $r \approx 0.10409$

Therefore, the IRR on this investment is approximately 10.41%.

Should the company make the investment? Yes, the company should likely make this investment.

Explanation: The IRR of 10.41% is higher than the company's required rate of return of 8.5%. The IRR represents the actual rate of return the investment is expected to generate. Since the expected return (10.41%) exceeds the minimum acceptable return (8.5%), the investment is considered profitable and should be undertaken, assuming the risk associated with the investment is comparable to other investments with a similar required return.

Situation 3: Common Stock Valuation

Question: What is the maximum price per share that your company should pay for the stock of Zorp Corporation, which paid a dividend of $4.25 last year, is currently selling for $36 per share, has a constant growth rate of 3% per year, and your company's required return on the stock is 11%? The stock will be held for 5 years and then sold.
Answer: To determine the maximum price the company should pay, we need to calculate the present value of all expected future cash flows from owning the stock for 5 years, discounted at the required rate of return. The cash flows will consist of the dividends received over the 5 years and the expected selling price at the end of year 5.

First, let's calculate the expected dividends for the next 5 years:
- $D_{1} = D_{0} \times (1 + g)^{1} = $4.25 \times (1.03)^{1} = $4.3775$
- $D_{2} = D_{0} \times (1 + g)^{2} = $4.25 \times (1.03)^{2} = $4.5088$
- $D_{3} = D_{0} \times (1 + g)^{3} = $4.25 \times (1.03)^{3} = $4.6441$
- $D_{4} = D_{0} \times (1 + g)^{4} = $4.25 \times (1.03)^{4} = $4.7834$
- $D_{5} = D_{0} \times (1 + g)^{5} = $4.25 \times (1.03)^{5} = $4.9269$
Next, we need to estimate the selling price of the stock at the end of year 5. We can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth) to estimate the price at that time, assuming the growth rate continues:

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

Where:
- $D_{6} = D_{5} \times (1 + g) = $4.9269 \times (1.03) = $5.0747$
- $r = Required Return = 11% = 0.11$
- $g = Growth Rate = 3% = 0.03$
$P_{5} = 0.11 - 0.03 $5.0747 = 0.08 $5.0747 \approx $63.43$

Now, we need to calculate the present value of the five dividends and the expected selling price, discounted at the required return of 11%:

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

$P V = ( 1.11 ) ^{1} $4.3775 + ( 1.11 ) ^{2} $4.5088 + ( 1.11 ) ^{3} $4.6441 + ( 1.11 ) ^{4} $4.7834 + ( 1.11 ) ^{5} $4.9269 + ( 1.11 ) ^{5} $63.43$

$P V = $3.9437 + $3.6586 + $3.3987 + $3.1618 + $2.9469 + $37.7165$

$P V \approx $54.83$

Explanation: Based on the expected future cash flows (dividends and selling price) discounted at the company's required return of 11%, the maximum price per share that the company should pay for the stock is approximately $54.83. The current market price of $36 is significantly lower than this calculated value, suggesting the stock might be undervalued based on the company's expectations and required return.

Situation 4: Zorp Corporation Bonds

Question 4a: What is the YTM on these bonds?
Answer 4a: The Yield to Maturity (YTM) is the total return anticipated on a bond if it is held until it matures. It takes into account the bond's current market price, par value, coupon interest rate, and time to maturity.

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

$P_{0} = t = 1 \sum n ( 1 + r ) ^{t} C + ( 1 + r ) ^{n} F V$

Where:
- $P_{0}$ = Current Market Price = $987
- $C$ = Annual Coupon Payment = 5% of $1,000 = $50
- $F V$ = Face Value (Par Value) = $1,000
- $n$ = Years to Maturity = 16
- $r$ = Yield to Maturity (what we need to find)
This equation cannot be easily solved directly for 'r', so we typically use a financial calculator or spreadsheet software to find the YTM.

Using a financial calculator or spreadsheet software, the YTM for these bonds is approximately 5.11%.
Question 4b: If the bonds are called immediately after the call protection period (in 4 years) at 105, what would be the yield to call (YTC)?
Answer 4b: The Yield to Call (YTC) is the total return anticipated on a bond if it is called before its maturity date. In this case, the call price is 105% of the par value, which is $1,000 \times 1.05 = $1,050. The call will occur in 4 years.

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

$P_{0} = t = 1 \sum 4 ( 1 + y ) ^{t} C + ( 1 + y ) ^{4} C a llP r i ce$

Where:
- $P_{0}$ = Current Market Price = $987
- $C$ = Annual Coupon Payment = $50
- $C a llP r i ce$ = $1,050
- $n$ = Years to Call = 4
- $y$ = Yield to Call (what we need to find)
Again, we typically use a financial calculator or spreadsheet software to find the YTC.

Using a financial calculator or spreadsheet software, the YTC for these bonds is approximately 6.74%.
Question 4c: If the bonds paid interest semiannually instead of annually, would the YTC, the YTM, or both change? Explain your answers.
Answer 4c: Both the YTM and the YTC would change if the bonds paid interest semiannually instead of annually.

Explanation:
- Yield to Maturity (YTM): When interest is paid semiannually, the following adjustments are made in the YTM calculation:
  - The number of periods doubles (16 years becomes 32 semiannual periods).
  - The semiannual coupon payment is half of the annual coupon payment ($50 / 2 = $25).
  - The discount rate (YTM) is also effectively halved for each semiannual period.
  To make the YTM comparable to an annual rate, the calculated semiannual yield is typically multiplied by 2 (the bond equivalent yield). However, the effective annual yield will be slightly higher than just doubling the semiannual rate due to the compounding effect. Therefore, the stated YTM would change.
- Yield to Call (YTC): Similarly, if interest is paid semiannually, the YTC calculation would also change:
  - The number of periods to the call date doubles (4 years becomes 8 semiannual periods).
  - The semiannual coupon payment is $25.
  - The discount rate (YTC) is effectively halved for each semiannual period.
  Again, the stated YTC (annualized) would be different to reflect the semiannual compounding.
In summary, the shift from annual to semiannual interest payments alters the timing and frequency of cash flows, which directly impacts the calculated discount rates (YTM and YTC) that equate the present value of these cash flows to the bond's current price. The more frequent compounding of interest leads to a slightly higher effective annual yield for a given stated annual rate.

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