Problem Set # 2 – Time Value of Money Solution

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Golden Gate University *

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300

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Finance

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Jan 9, 2024

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Corporate Finance FI-300 1) What is an opportunity cost rate? How is this rate used in discounted cash flow analysis? Is the opportunity rate a single number that is used to evaluate all potential investments? Ans- Opportunity cost rate is the anticipated profits that an investor, individual or a business owner sacrifices in order to yield from another investment. This is calculated assuming that the risk involved in both investments is the same. It is an excellent tool used by companies to make a decisive choice of one investment over the other and understand the opportunities that they might end up missing. Discounted Cash Flow Analysis - Discounted Cashflow Analysis is a valuation Method which is used to determine the valuation of an investment based on its expected Future cash flows. It helps in determining the value of an investment today based on how much cash flows that investment will generate in the future. Opportunity Cost plays an important role in DCF Analysis. Discounted Cash Flow Analysis uses a discounted rate to evaluate the present value based on future value, this discount rate is selected between alternative investments using the opportunity cost. For example, $100 with a discount rate of 10% would be 110$ in a year thus indoor to select the investments we need opportunity cost rate. While Opportunity Cost rate is not included in accounting profits and is kept away from the external Financing of the company, Opportunity Cost is not a fixed rate rather a dynamic rate that changes depending upon the riskiness and maturity of the investment in question. Another factor that influences the opportunity rate is the inflationary expectations.

2) If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain. (Hint: Solve for the interest rate. Make sure you put the PV or FV as a negative number.) Ans - The example stated above is correct because it would provide an annual return of 7.18%. (Solved in excel) 3) Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays interest compounded daily? Explain. Ans - I would prefer to have a savings account that pays interest compounded daily. Compounding daily means that the interest is calculated and added to the account balance every day, allowing for faster growth of the savings. This frequency of compounding results in the account earning more interest over time compared to semiannual compounding. By compounding daily, even the small amounts of interest earned each day contribute to the overall growth of the savings. This compounding effect can help maximize the returns and lead to a higher final balance in the account. On the other hand, with semiannual compounding, the interest is only added twice a year, which means the account has fewer opportunities to generate interest on the accumulated interest. Assuming an investment worth $1000 with a semiannual rate of 5% the total money yielded after 10 years would be $1,628.89. On the other hand, a similar investment in an account that yields interest daily would return $1,648.66. This is because the greater the number of compounding periods, the more the interest generated would be. (Solved in excel) 4) We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% how long will it take sales to double? (Hint: Assume that your current level of sales is at 100 units and find out how long it will take to get to 200 units if sales grow at 20% each year. Solve for N. Make sure you put the PV or FV as a negative number.) Ans - It will take 3.8 Years for the amount to double. (Solved in excel)

5) If you want an investment to double in 3 years, what interest rate must it earn? (Hint: Solve for the interest rate) Ans- Interest Rate - 26% (Solved in excel) 6) Find the FV of $1000 invested to earn 10% annually 5 years from now. (Assume this is a single payment not an annuity). Ans- $1,610.51 (Solved in excel) 7) Find the PV of $1000 due in 5 years if the discount rate is 10% per year. (Assume this is a single payment not an annuity). Ans- $620.9 (Solved in excel) 8) What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? Ans- $1,725.22 (Solved in excel) 9) While Jack was a student at the University of Georgia she borrowed $12,000 in student loans at an annual interest rate of 9%. If Jack repays $1,500 per year then how long (to the nearest year) will it take him to repay the loan? Ans- Around 15 years (Solved in excel) 10) What is the present value of a perpetuity of $100 if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity? Ans- When the discount rate of 7% is doubled to 14% the PV of perpetuity of $100 is reduced from $1,428.57 to $714.29 thus falling to half the previous amount. (Solved in excel)

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11) Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR (Nominal Interest Rate) is stated to be 18.00%, with interest compounded monthly, what is the card's EFF%? Ans- 19.56% would be the EFF% (Solved in excel) 12) When Jane and Patrick Baker were “house hunting” five years ago, the fixed rate on a 30- year mortgage was 6% APR (Nominal Interest Rate) with monthly compounding. After walking through many homes, they finally reached a consensus and decided to buy a $500,000 home. The couple decided to put 20% down payment and took the 30-year mortgage with monthly payments. a) What is Jane and Patrick’s monthly mortgage payment? b) Construct an amortization schedule in excel for the loan. c) During the first 5 years, how much has the couple paid towards the mortgage? d) What proportion of this was applied toward interest? What is the balance on their loan today? Ans- a) The monthly mortgage payment for them is $2,398.20 b) Solved in Excel File c)$143,892.12 (Solved in Excel) d)Out of the total Amt paid $27,782.57 was the principal paid, while the rest i.e. 80.69% ($116,109.55) of the montage paid was the interest paid. (Solved in excel)