6005 Basics of Financial Management Midterm Review Part 2

Here are the detailed calculations along with the problem questions:

Annuity Due Calculation

• Background Normalization: Set period to BGN to standardize the annuity calculations.

• Future Value (FV): $12,000.

• Interest Rate (I/y): 6.8%, reflecting the annual growth rate of the investment.

• Number of Periods (N): 4, indicating the number of years the annuity is paid.

• Calculation Method: Calculate payment using financial calculator (CPT PMT) for obtaining equal payments over the specified periods.

Problem Question: "What is the monthly payment for an annuity due with a future value of $12,000, an interest rate of 6.8%, for 4 periods?"

Lease Value Calculation

• Lease Duration: 20 years, the total timeframe for lease payments.

• First Payment: $2,000, representing the initial payment at the start of the lease.

• Annual Increase: 4% increase each subsequent year, impacting total payments made over the lease duration.

• Discount Rate: 9%, the rate used to bring future cash flows to present value.

• Calculation:

  • Present Value of Growing Annuity:

    [ PVAn = \frac{CF_1}{(i - g)} = \frac{2000}{(0.09 - 0.04)} = 40,000 ]

    • Adjusted Factor Calculation: [ (1+g)/(1+i)^n = \frac{1.04}{1.09}^{20} \approx 0.3910 ]

    • Final present value calculation: [ PV = 40,000 * (1 - 0.3910) = 24,360 ]

Problem Question: "Calculate the present value of a lease with a first payment of $2,000, increasing by 4% annually over 20 years, discounted at 9%. What is the present value?"

Growing Perpetuity Calculation

• Cash Flow in Year 1 (CF1): $25,000.

• Annual Growth Rate (g): 2.5% is the growth expected in the cash flow.

• Discount Rate (i): 7.5% signifies the required rate of return for the investment.

• Present Value of Growing Perpetuity Formula:

  [ PV = \frac{CF_1}{(i - g)} = \frac{25000}{(0.075 - 0.025)} = 500000 ]

Problem Question: "What is the present value of a growing perpetuity that starts with a cash flow of $25,000 and grows by 2.5% annually with a discount rate of 7.5%?"

Loan Payment Calculation

• Monthly Payment: $17,384 for a duration of 3 years indicates regular payments made towards loan repayment.

• Interest Rate: 8.40% is the nominal interest charged on the loan.

• Effective Annual Rate (EAR):

  [ \text{EAR} = \left[1 + \frac{0.084}{12}\right]^{12} - 1 \approx 0.0873 ] or 8.73%, providing the true cost of the loan on an annualized basis.

Conclusion: Correct answer results in B. Problem Question: "What is the effective annual rate on the loan?"

Bond Pricing Calculation

• Bond Duration: 20-year bonds with a semiannual interest payment of 7.8%.

• Market Rate: Currently set at 7%, reflects the prevailing yield on comparable investments.

• Semiannual coupon payment:[ \text{Coupon Payment} = 1000 \times \frac{0.078}{2} = 39.00 ]

  • This represents the payment received every six months.

  • Next, calculate the present value of the bond cash flows combining coupon payments and face value.

Problem Question: "Calculate the present value of the bond cash flows."

Bond Purchase Analysis

• Price Offered: $943.22 for a bond maturing in 7 years with a 9% coupon rate.

• Required Market Yield: 10% signifies the yield expected by investors.

• Present Value of Bond equation:

  [ PV = C \times \left(1 - (1 + r)^{-n}\right) / r + \frac{F}{(1+r)^n} ]Where (C = 90), (r = 0.10), (n = 7) and (F = 1000)

• Plug Values into the Formula: [ PV = 90 \times \left(1 - (1 + 0.10)^{-7}\right) / 0.10 + \frac{1000}{(1+0.10)^7} \approx 921 ]

• Conclusion: The bond appears overpriced, thus the decision is a 'No'; correct answer: B. Problem Question: "Is the bond overpriced based on your calculations?"

Zero Coupon Bond Pricing

• Face Value: $1,000, the amount payable at maturity.

• Maturity Term: 5 years, representing the time until payment.

• Opportunity Cost: 8.5%.

• Current Market Price Calculation: [ P = \frac{F}{(1+r)^n} = \frac{1000}{(1+0.085)^5} \approx 665 ]

Problem Question: "What is the current market price of the zero coupon bond?"

Market Yield Calculation

• Investment: A bond yielding 7% with a current price of $927.23.

• Yield Calculation: Therefore, solving for yield (YTM):

  [ Y = \frac{C + \frac{F-P}{N}}{(P + F) / 2} ]

• Replace Values:

  [ Y = \frac{70 + \frac{1000-927.23}{10}}{(927.23 + 1000) / 2} \approx 0.084 ] thus, YTM = 8.4%.

Problem Question: "Determine the market yield for this bond."

Yield Calculation on Bond Investment

• Bond Duration: 4-year bond paying 11% coupon at a current selling price of $962.13.

• Yield Calculation:

  • Calculate yield (YTM) by solving:

    [ Y = \frac{C + (F-P)/N}{(P + F)/2} = \frac{(110 + (1000-962.13)/4)}{(962.13 + 1000)/2} \approx 0.122 ] thus Yield = 12.2%.

Problem Question: "What is the yield on the bond investment?"

Effective Annual Yield Calculation

• Annual Yield: 6.4% with semiannual payments.

• Effective Annual Yield:

  [ \text{EAY} = \left(1 + \frac{0.064}{2}\right)^2 - 1 \approx 0.065 ]

Problem Question: "Calculate the effective annual yield based on the given rates."

Stock Valuation with No Growth

• Last Dividend: $4.50.

• Discount Rate: 9%.

• Price Calculation: Using the formula:

  [ Price = \frac{Dividend}{Discount Rate} = \frac{4.50}{0.09} = 50.00 ]

Problem Question: "What is the price of the stock with no growth?"

Dividend Calculation from Stock Price

• Selling Price: $46.88.

• Required Return: 16%.

• Dividend Calculation:

  [ Dividend = Price \times Required Return = 46.88 \times 0.16 = 7.50 ]

Problem Question: "How much dividend is associated with the stock selling at $46.88?"

Current Price of Stock with Growth

• Last Dividend: $4.45.

• Growth Rate: 8%.

• Discount Rate: 14%.

• Current Price Calculation:

  [ Price = \frac{D_0 \times (1 + g)}{r - g} = \frac{4.45 \times 1.08}{0.14 - 0.08} = 80.00 ]

Problem Question: "What is the current price of the stock taking growth into account?"

Expected Dividend Calculation

• Stock Price: $63.25.

• Growth Rate: 7%.

• Rate of Return: 17%.

• Expected Dividend Calculation:

  [ Expected Dividend = Price \times (r - g) = 63.25 \times 0.07 = 6.33 ]

Problem Question: "What is the expected dividend based on the stock price and growth rate?"

Future Price Calculation of Increasing Dividend

• Dividend Growth: 8%.

• Last Dividend: $3.

• Future Price Calculation:

  [ F = D_0 \times (1+g)^n = 3 \times (1+0.08) = 58.31 ]

Problem Question: "What will be the future stock price given the last dividend and growth rate?"

Stock Price from Multiple Dividends

• Future Dividends: Estimated for the first four years followed by a constant payment rate.

• Present Value Calculation:

  [ PV = \sum_{t=1}^{4}\frac{D_t}{(1+r)^t} + \frac{D_{Constant}}{(1+r)^n} \approx 69.41 ]

Problem Question: "What is the resulting stock price from multiple future dividends?"

Growth Rate Evaluation

• Forecasted Dividend Growth Rates: Expected for the first three years.

• Market Stock Value Calculation:

  [ Market Value = \sum_{t=1}^{3}D_t \times (1+g)^t + D_{Constant} ] leads to approximately $36.86.

Problem Question: "What is the evaluated market stock value based on projected growth rates?"

Valuation of Preferred Stock

• Preferred Stock: Assessed at 8.5% required return.

• Price Calculation:

  [ Price = \frac{D}{r} = \frac{D}{0.085} \approx 65.88 ]

Problem Question: "What is the current price of the preferred stock based on the required return?"

Dividend from Preferred Stock Price

• Current Price: $110.35.

• Required Yield: Leading to:

  [ Dividend = Price \times Required Yield = 110.35 \times 0.085 \approx 10.76 ]

Problem Question: "What dividend is associated with the preferred stock priced at $110.35?"