Problem 5.17: Your Finance Textbook Sold 46,000 Copies ✓ Solved

Problem 5.17: Your finance text book sold 46,000 copies in i

Problem 5.17: Your finance text book sold 46,000 copies in its first year. The publishing company expects sales to grow 17.0% for the next three years and by 6.0% in the fourth year. Calculate the number of copies expected to be sold in year 3 and in year 4. Round final answers to the nearest whole number.

Problem 5.21: Find the present value of $3,200 under each of the following:

a. 8.9% compounded monthly for 5 years.

b. 6.6% compounded quarterly for 8 years.

c. 4.3% compounded daily for 4 years.

d. 5.7% compounded continuously for 3 years.

Round final answers to the nearest penny.

Problem 6.19: Trigen Corp. will invest cash flows of $776,142; $931,217; $682,429; $818,400; $1,239,644; and $1,617,848 over the next six years. If the interest rate is 5.82%, what is the future value of these investment cash flows six years from today? Round to 2 decimal places.

Problem 6.27: You are offered $527,000 today plus $527,000 at the end of each of the following six years. If the interest rate is 8%, what is the present value of this cash flow stream? Round to the nearest whole dollar.

Problem 7.16: Given states of the economy with probabilities and returns: Boom (0.4, 25%), Good (0.4, 15%), Level (0.1, 10%), Slump (0.1, -5%), calculate the expected return. Round to 3 decimal places.

Problem 8.24: Trevor bought 10-year bonds five years ago for $915.52. The bonds make semiannual coupon payments at 8.4%. If current price is $1,002.35, what is the effective annual yield by selling the bonds today? Round intermediate calculations to 4 decimals and final answer to 2 decimal places.

Problem 9.15: First Bank issued perpetual preferred stock with $100 par and a quarterly dividend of $1.65. Given required return of 14.5%, what is the current price? Round to 2 decimals.

Week 5 Quiz Multiple Choice: Provide answers to the following selected questions:

- Genaro's maximum purchase price given he needs 40% return, expected sale $150,000 and rental income $25,000.

- Define the process of identifying the bundle of projects that creates greatest total value and allocates available capital.

- Profitability index for project with initial cost $1,200,000 and net cash flows $300,000 per year for 6 years at 10% discount rate.

- Causes of capital rationing.

- Given WACC 19.75%, equity $75m, debt $25m, cost of debt 7%, find cost of equity.

- YTM for Bellamee, Inc. semiannual bonds priced at $920.87 with 5 years to maturity and 7% coupon.

- After-tax cost of debt for Beckham Corporation: semiannual bonds, 13 years to maturity, price $746.16, coupon 8.5%, tax rate 35%.

- Find firm's beta if cost of equity 22.8%, risk-free 10%, market return 18%.

- Which type of project uses the highest cost of capital when evaluating: efficiency, extension, market expansion, or new product projects.

Week 5 Learning Team Reflection: Write a 150–170 word summary discussing corporate finance challenges faced by a company related to cost of capital.

Paper For Above Instructions

Overview

This paper solves each listed problem sequentially, showing formulas, numeric results, and brief interpretation. All monetary answers are rounded per instructions. Standard time value of money and expected-return formulas are used (Ross et al., 2019; Brealey, Myers & Allen, 2020).

Problem 5.17 — Sales Growth (Year 3 and Year 4)

Interpretation: Year 1 sales = 46,000. The next three years (years 2–4) grow at 17%. Therefore:

Year 3 sales = 46,000 × (1.17)² = 46,000 × 1.3689 = 62,949 copies (rounded).

Year 4 sales = 46,000 × (1.17)³ = 46,000 × 1.600613 = 73,628 copies (rounded).

These projections use compound growth per period (standard growth modeling) (Brigham & Ehrhardt, 2019).

Problem 5.21 — Present Values of $3,200

General formula (discrete compounding): PV = FV / (1 + r/m)^{m·t}. For continuous compounding PV = FV · e^{-r·t} (Bodie, Kane & Marcus, 2019).

  • a) 8.9% compounded monthly, 5 years: periodic = 0.089/12. PV ≈ $2,054.24.
  • b) 6.6% compounded quarterly, 8 years: periodic = 0.066/4. PV ≈ $1,895.89.
  • c) 4.3% compounded daily, 4 years: periodic = 0.043/365. PV ≈ $2,693.42.
  • d) 5.7% continuously compounded, 3 years: PV = 3,200·e^{-0.057·3} ≈ $2,696.96.

Each PV computed using the respective discount factor formula (Investopedia, 2021).

Problem 6.19 — Future Value of Uneven Cash Flows

Each cash flow is compounded forward to year 6: FV = Σ CF_t · (1 + r)^{6 - t} where t is year of the cash flow (years 1–6). Using r = 5.82%:

  • Year1 contribution ≈ $776,142·(1.0582)^5 = $1,032,215
  • Year2 ≈ $931,217·(1.0582)^4 = $1,169,323
  • Year3 ≈ $682,429·(1.0582)^3 = $809,203
  • Year4 ≈ $818,400·(1.0582)^2 = $916,428
  • Year5 ≈ $1,239,644·(1.0582)^1 = $1,311,793
  • Year6 ≈ $1,617,848 = $1,617,848

Total FV ≈ $6,856,810.00 (rounded to two decimals). This uses standard compounding for irregular deposits (Ross et al., 2019).

Problem 6.27 — Present Value of Mixed Stream

Offer: $527,000 today (t=0) plus six end-of-year payments of $527,000 (years 1–6). PV = 527,000 + 527,000·[1 − (1+0.08)^{-6}]/0.08.

Compute annuity PV factor ≈ 4.626275 → PV of annuity ≈ $2,438,041. Add immediate 527,000 → Total PV ≈ $2,965,041 (nearest dollar).

Problem 7.16 — Expected Return

Expected return = Σ p_i·r_i = 0.4·0.25 + 0.4·0.15 + 0.1·0.10 + 0.1·(−0.05) = 0.165 → 16.5%.

As decimal, rounded to three decimals = 0.165 (standard expectation calculation) (Brealey et al., 2020).

Problem 8.24 — Bond Yield (Effective Annual Yield)

Assume $1,000 par. Semiannual coupon = 0.084·1000/2 = $42. Remaining periods = 10. Solve for semiannual yield i from price = 1,002.35. Numerical solution gives i ≈ 0.041713 per semiannual period. Effective annual yield = (1 + i)^2 − 1 ≈ 8.52% (rounded to 2 decimals).

YTM solved by standard bond pricing inversion (Fabozzi, 2016).

Problem 9.15 — Perpetual Preferred Stock Price

Quarterly dividend = $1.65, required annual return = 14.5% → quarterly required return = 0.145/4 = 0.03625. Perpetuity price = D_quarter / r_quarter = 1.65 / 0.03625 ≈ $45.52.

This follows the perpetual dividend valuation formula (Brealey & Myers, 2020).

Week 5 Quiz — Selected Answers and Brief Workings

  • Genaro max price: Solve (150,000 + 25,000 − P)/P = 0.40 → P = $125,000.
  • Process of selecting project bundle and allocating capital = capital rationing.
  • Profitability index: PV of 6-year annuity of $300,000 at 10% ≈ $1,306,578; PI = 1,306,578 / 1,200,000 ≈ 1.09.
  • Cause of capital rationing: having more than one project with positive NPVs and limited capital.
  • WACC problem: 0.75·r_e + 0.25·0.07 = 0.1975 → r_e = 24.0%.
  • Bellamee bond YTM: approx 9.0% (annual) given semiannual yield ≈ 4.5%.
  • Beckham after-tax cost of debt: pre-tax nominal YTM ≈ 12.50% → after-tax = 12.50%·(1 − 0.35) = 8.125%.
  • Firm beta (CAPM): beta = (0.228 − 0.10)/(0.18 − 0.10) = 1.60.
  • Project type with highest cost of capital: new product projects (highest risk).

Week 5 Learning Team Reflection (approx. 160 words)

Companies face several corporate finance challenges related to cost of capital. First, accurately estimating the cost of equity and debt is difficult because market conditions, risk premia, and firm-specific beta fluctuate; incorrect estimates can misprice projects and lead to value-destroying investment decisions (Brealey et al., 2020). Second, choosing appropriate project-specific discount rates is challenging when projects have different risk profiles; using a single corporate WACC for all projects can under- or overstate project value (Ross et al., 2019). Third, capital rationing and budget constraints force managers to prioritize projects, which raises portfolio optimization issues and requires estimating incremental returns and correlations across projects (Brigham & Ehrhardt, 2019). Finally, tax policy, leverage decisions, and market volatility affect after-tax costs and the firm’s optimal capital structure; balancing tax benefits of debt against financial distress costs remains an ongoing trade-off (Modigliani & Miller theory extensions) (Brealey & Myers, 2020).

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Brigham, E. F., & Ehrhardt, M. C. (2019). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2019). Investments (11th ed.). McGraw-Hill Education.
  • Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies (9th ed.). Pearson.
  • Investopedia. (2021). Time Value of Money. https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Investopedia. (2021). Present Value. https://www.investopedia.com/terms/p/presentvalue.asp
  • CFA Institute. (2019). The Capital Asset Pricing Model (CAPM) and cost of capital materials. https://www.cfainstitute.org
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley.
  • Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. American Economic Review, 48(3), 261–297.

Related Assignments