Problem 517: Your Finance Textbook Sold 45,000 Copies

Problem 517your Finance Text Book Sold 45000 Copies In Its First Yea

Problem 517your Finance Text Book sold 45,000 copies in its first year. The publishing company expects the sales to grow at a rate of 16.0 percent for the next three years, and by 13.0 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in year 3 and 4. (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answers to the nearest whole number.) Number of copies sold after 3 years ___ Number of copies sold in the fourth year ____ Problem 5.21 Find the present value of $5,200 under each of the following rates and periods. (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.) a. 8.9 percent compounded monthly for five years. Present Value ____ b. 6.6 percent compounded quarterly for eight years. Present Value ____ c. 4.3 percent compounded daily for four years. Present Value ____ d. 5.7 percent compounded continuously for three years. Present Value ____ Problem 6.19 Trigen Corp. management will invest cash flows of $590,849, $509,135, $476,409, $818,400, $1,239,644, and $1,617,848 in research and development over the next six years. If the appropriate interest rate is 8.24 percent, what is the future value of these investment cash flows six years from today? (Round answer to 2 decimal places, e.g. 15.25.) Future Value ____ Problem 6.27 You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into their systems and is offering to pay you $546,000 today, plus $546,000 at the end of each of the following six years for permission to do this. If the appropriate interest rate is 7 percent, what is the present value of the cash flow stream that the company is offering you? (Round answer to the nearest whole dollar, e.g. 5,275.) Future Value ____ Problem 7.16 Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find Probability Return Boom 0.2 25.00% Good 0.3 15.00% Level 0.4 10.00% Slump 0.1 -5.00% What is the expected return on Barbara’s investment? (Round answer to 3 decimal places, e.g. 0.076.) Expected Return ____ What is the standard deviation of the return on Barbara's investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Standard Deviation ____ Problem 8.24 Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $981.61. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $1,023.62, what is the yield that Trevor would earn by selling the bonds today? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.) Effective Annual Yield ____ Problem 9.15 The First Bank of Ellicott City has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 11.5 percent? (Round answer to 2 decimal places, e.g. 15.25.) Current Price ____

Paper For Above instruction

This collection of finance problems encompasses various key concepts integral to financial analysis and investment decision-making, including growth calculations, present and future value computations, investment valuation, expected return estimation, standard deviation of returns, bond yield calculations, and valuation of preferred stock. Addressing these problems provides a comprehensive review of essential financial mathematics techniques, which are foundational for professionals and students in finance and investment fields.

The first problem involves forecasting sales volume based on growth rates. Starting with 45,000 copies sold in the first year, the goal is to determine sales for years three and four, given annual growth rates of 16% for the initial three years and 13% in the fourth. To achieve this, the sales after initial growth are calculated sequentially using the formula:

\[ \text{Future Sales} = \text{Current Sales} \times (1 + \text{Growth Rate}) \]

Applying this iteratively, sales after year 1 are 45,000 copies. Year 2 sales are 45,000 × 1.16 = 52,200 copies, Year 3 sales are 52,200 × 1.16 ≈ 60,552 copies, providing the expected sales figure for year 3. For year 4, the sales are computed based on Year 3 sales multiplied by 1.13, yielding approximately 68,222 copies.

The second problem deals with the present value of a future sum of money under different compounding interest rates and periods. It requires utilizing the present value formula:

\[ PV = \frac{FV}{(1 + i/n)^{nt}} \]

Where FV is the future value, i is the annual nominal interest rate, n is the number of compounding periods per year, and t is the number of years. For continuous compounding, the formula used is:

\[ PV = FV \times e^{-rt} \]

Calculations involve substituting the parameters for each scenario and rounding the results to the nearest penny.

The third problem focuses on compounding cash flows over multiple years at a given interest rate to find the future value. Using the formula:

\[ FV = PV \times (1 + r)^t \]

the future value of specific cash flows is determined. Summing these to obtain the total future value reflects the growth of investments over time, considering compound interest.

The fourth problem involves the future value of multiple cash flows invested over different years. Applying the future value formula for each cash flow, discounted or compounded to the same future point (six years), results in the aggregate future value, demonstrating the power of compound interest over time.

The fifth problem addresses valuing a stream of cash flows—specifically, a series of payments over multiple years—by calculating their present value using the present value of an annuity formula:

\[ PV = P \times \frac{1 - (1 + r)^{-n}}{r} \]

where P is the periodic payment, r is the periodic rate, and n is the number of payments. This formula helps in deriving the current worth of recurring cash flows at different discount rates.

The sixth problem is about future value calculation of multiple cash flows over time, considering an interest rate. Each cash flow is compounded to year six, and their sum provides the total future value. This entails individual calculations for each cash flow, highlighting the effect of time value of money.

The seventh problem involves probabilistic analysis, calculating the expected return and standard deviation of a stock based on different economic states. The expected return combines the probabilities and returns for each state:

\[ E(R) = \sum_{i} P_i \times R_i \]

where \( P_i \) is the probability of state i, and \( R_i \) is the return in that state. The standard deviation measures the spread of returns, calculated using the variance:

\[ \sigma = \sqrt{\sum_{i} P_i \times (R_i - E(R))^2} \]

Careful computation yields insights into the risk and reward profile of the investment.

In the eighth problem, bond yield calculation involves estimating the yield to maturity (YTM) based on current bond prices, coupon payments, and time to maturity. Since bonds have semiannual coupons, the rate is annualized but computed on a semiannual basis. By solving the bond pricing equation:

\[ P = \sum_{t=1}^{N} \frac{C}{(1 + y/2)^t} + \frac{F}{(1 + y/2)^N} \]

where P is current price, C is semiannual coupon, F is face value, N is total number of periods, and y is the YTM, iterative methods or financial calculators approximate y. The effective annual yield then adjusts the semiannual yield to an annual basis.

The final problem pertains to valuing perpetual preferred stock—equity that pays fixed dividends forever—using the dividend discount model:

\[ P_0 = \frac{D}{r} \]

where D is the quarterly dividend and r is the required annual return, adjusted to match the dividend payment frequency. This calculation determines the fair current price of the preferred stock.

Overall, these problems collectively highlight essential financial computations, illustrating how to evaluate investments, forecast sales, analyze risk, and determine valuation metrics under different assumptions and market conditions. Mastery of these techniques is critical for financial decision-makers aiming to optimize investment portfolios, manage risk, and accurately value financial assets.

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