Financial Instrument Valuation and Market Analysis

Written on June 14, 2025 in English with a size of 9.33 KB

Bond and Stock Valuation Fundamentals

Taxable Equivalent Yield for Bonds

Question: If you can purchase a municipal bond which returns 5.6% and you are in the 25% tax bracket, what rate of return would you require on a corporate bond?

Key Concepts:

Municipal bonds are generally tax-exempt at the federal level and often at the state and local levels if issued within your state of residence.
Corporate bonds are typically subject to federal, state, and local income taxes.

Formula:

Taxable Equivalent Yield (TEY) = Municipal Rate / (1 - Tax Rate)

Calculation:

TEY = 5.6% / (1 - 25%)

TEY = 5.6% / 0.75

Result: 7.47%

Gamemasters Stock Valuation (Gordon Growth Model)

Question: Analysts have forecasted Gamemasters will grow at a rate of 8% into the future. Gamemasters recently paid a dividend of $2.15 and investors require a return of 14.5%. What is the value of this stock?

Formula (Gordon Growth Model):

P₀ = D₁ / (r - g)

Where:

P₀ = Current Stock Price
D₁ = Expected Dividend in the next period (D₀ * (1 + g))
r = Required Rate of Return
g = Constant Growth Rate of Dividends

Calculation:

D₀ = $2.15
g = 8% (0.08)
r = 14.5% (0.145)
D₁ = $2.15 * (1 + 0.08) = $2.322

P₀ = $2.322 / (0.145 - 0.08)

P₀ = $2.322 / 0.065

Result: $35.72

Multi-Stage Dividend Discount Model for Stock Valuation

Question: You are interested in a fast-expanding company that is currently growing at a rate of 30% and is expected to continue to grow at that rate for another three years before slowing down to a rate of 7.5%. If investors expect a return of 12% and the company recently paid a dividend of $1.75, what is the value of the stock?

Key Information:

Dividend Paid (D₀): $1.75
High Growth Rate (g₁): 30% for 3 years
Stable Growth Rate (g₂): 7.5%
Required Rate of Return (r): 12%

Calculation Steps:

Calculate Dividends during High Growth Period:
- D₁ = D₀ * (1 + g₁) = $1.75 * (1 + 0.30) = $2.275
- D₂ = D₁ * (1 + g₁) = $2.275 * (1 + 0.30) = $2.9575
- D₃ = D₂ * (1 + g₁) = $2.9575 * (1 + 0.30) = $3.84475
Calculate Present Value of High Growth Dividends:
- PV(D₁) = D₁ / (1 + r)¹ = $2.275 / (1.12)¹ = $2.03
- PV(D₂) = D₂ / (1 + r)² = $2.9575 / (1.12)² = $2.36
- PV(D₃) = D₃ / (1 + r)³ = $3.84475 / (1.12)³ = $2.74
Calculate Terminal Value (P₃) at the end of Year 3:
P₃ = D₄ / (r - g₂)
- D₄ = D₃ * (1 + g₂) = $3.84475 * (1 + 0.075) = $4.13210625
- P₃ = $4.13210625 / (0.12 - 0.075) = $4.13210625 / 0.045 = $91.82
Calculate Present Value of Terminal Value:
PV(P₃) = P₃ / (1 + r)³ = $91.82 / (1.12)³ = $65.36
Sum Present Values for Total Stock Value:
Total Stock Value = PV(D₁) + PV(D₂) + PV(D₃) + PV(P₃)
Total Stock Value = $2.03 + $2.36 + $2.74 + $65.36

Result: $72.49

Bond Maturity Period Calculation

Question: What is the years to maturity on a bond issued November 1, 2001, and due November 1, 2021?

Calculation:

Maturity Year - Issue Year = 2021 - 2001

Result: 20 years

Zero Coupon Bond Pricing

Question: What is the price of a zero coupon bond that was issued for $1,000 and matures in 14 years if the market interest rate is 9%? (Calculate as semi-annual)

Key Information:

Face Value (FV): $1,000
Maturity (Years): 14
Annual Market Rate: 9%

Calculation Steps:

Semi-annual Rate (r) = 9% / 2 = 4.5% (0.045)
Number of Periods (n) = 14 years * 2 periods/year = 28 periods
Payment (PMT) = $0 (zero coupon bond)

Formula:

Present Value (PV) = FV / (1 + r)ⁿ

Calculation:

PV = $1,000 / (1 + 0.045)²⁸

Result: $291.57

Stock Price from P/E Ratio

Question: Dell Computers reported earnings per share to be $5.85 this year. If the company P/E ratio is 28, what is the price of the stock?

Formula:

Stock Price = P/E Ratio * Earnings Per Share (EPS)

Calculation:

Stock Price = 28 * $5.85

Result: $163.80

TIPS Bond Par Value and Interest Payment

Question: A TIPS bond was issued with a CPI of 122.69 and a coupon of 6.5%. One year later the CPI is 128.32. What is the par value of the bond and how much interest will be paid (assume semi-annual interest)?

Key Information:

Initial CPI: 122.69
Current CPI: 128.32
Coupon Rate: 6.5%
Original Par Value: $1,000 (standard assumption for bonds)

Calculation Steps:

Calculate Adjusted Par Value:
Adjusted Par = Original Par * (Current CPI / Initial CPI)
Adjusted Par = $1,000 * (128.32 / 122.69) = $1,045.89
Calculate Semi-annual Interest Payment:
Interest Payment = (Adjusted Par * Coupon Rate) / 2
Interest Payment = ($1,045.89 * 0.065) / 2 = $33.99

Results:

Adjusted Par Value: $1,045.89
Semi-annual Interest Payment: $33.99

Current Yield on a Bond

Question: What is the current yield on a bond quoted at 98.91 if the bond pays a coupon of 6.54%?

Key Information:

Quoted Price: 98.91 (represents 98.91% of par value)
Coupon Rate: 6.54%
Assumed Par Value: $1,000

Calculation Steps:

Calculate Current Market Price:
Current Market Price = Quoted Price * (Par Value / 100)
Current Market Price = 98.91 * ($1,000 / 100) = $989.10
Calculate Annual Interest Payment:
Annual Interest = Coupon Rate * Par Value
Annual Interest = 0.0654 * $1,000 = $65.40
Calculate Current Yield:
Current Yield = Annual Interest / Current Market Price
Current Yield = $65.40 / $989.10

Result: 6.61%

Stock Purchase Cost (Bid and Ask Prices)

Question: If you buy 200 shares of a stock with bid and ask prices of $77.23 and $77.28, respectively, how much will you pay?

Key Concepts:

The bid price is the highest price a buyer is willing to pay for a security.
The ask price (or offer price) is the lowest price a seller is willing to accept for a security.
When you buy shares, you pay the ask price.

Calculation:

Total Cost = Number of Shares * Ask Price

Total Cost = 200 * $77.28

Result: $15,456.00

Preferred Stock Valuation

Question: If Home Depot has an 8.75% preferred stock with a par value of $100, what would you pay if the market rate is 6.5%?

Key Information:

Par Value: $100
Coupon Rate: 8.75%
Market Rate (Required Rate of Return): 6.5%

Calculation Steps:

Calculate Annual Dividend:
Annual Dividend = Par Value * Coupon Rate
Annual Dividend = $100 * 0.0875 = $8.75
Calculate Preferred Stock Value:
Preferred Stock Value = Annual Dividend / Market Rate
Preferred Stock Value = $8.75 / 0.065

Result: $134.62

Callable Bond Payout Calculation

Question: You own a callable bond that pays 10% annual coupon and it has a one-year interest penalty if it is called early. If it is called early, how much will you receive?

Key Concepts:

A callable bond gives the issuer the right to redeem the bond before its maturity date.
A call premium is an amount paid to the bondholder as compensation for the early redemption, often expressed as one year's interest.
Assumed Par Value: $1,000

Calculation:

Annual Interest = Par Value * Coupon Rate = $1,000 * 0.10 = $100

Amount Received = Par Value + One-Year Interest Penalty

Amount Received = $1,000 + $100

Result: $1,100.00

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