Time Value of Money Kieso Intermediate Accounting 170 Must be submitted through Canvas in the form of an Excel worksheet no later than April 7,2021. Students will be assigned to groups of three or four students and should plan to work together (virtually). Each group is responsible for submitting one final EXCEL spreadsheet with their answers to the following questions. Ignore income tax considerations in all scenarios below. 1. Future Value of a Single Sum. a. Watson, Inc. has an opportunity to invest $200,000 for five years at 5.25%, compounded annually. How much will Watson's investment be worth at the end of five years? b. Assume the same facts as in part a, except change the interest rate to 4,33%. How much is the investment worth after five years? c. Morgan has just received a $6,000 bonus from her company. If she invests the bonus at 4.10% for four years, how much will her investment be worth at the end of that time? 2. Present Value of a Single Sum a. Springfield wishes to match a state investment in a solar farm in four years. In order to accomplish this, Springfield must have $3,000,000 to invest at that time. How much must Springfield invest today at 4.25% in order to meet that goal? b. Your company estimates that it will need to replace its warehouse software in three years, at a cost of $225,000. Your CEO asks how much the company should invest now at an annual interest rate of 5.25% in order to have that amount available in three years. Provide her with an answer. CA baseball team has written a $10,000,000 performance bonus into a key player's contract. The player will receive the bonus if he hits 150 home runs over the next five years. The team believes the player will meet this target. The team can invest funds at 4,40%. How much should the team invest today in order to have the amount available to pay the bonus in five years. In other words, assuming the player will hit the requisite number of home runs, what is the present value of the commitment the team has made? 3. Solving for interest rate or number of periods a. A local museum wishes to invest $125,000 of endowed funds for 8 years, with a goal of having $200,000 at the end of that time. At what interest rate, compounded annually, would the museum need to invest the funds to achieve this goal? b. Assume the museum in part a knows, instead, that it can earn 6.25%, compounded annually, on its endowment of $125,000. How long (in years) will it take the endowment to grow to $200,000? 5. Compounding - Assume Lee, Inc. borrows $500,000 at 5.27% interest, compounded semiannually (twice per year). Lee, Inc. will repay the debt in a lump-sum at the end of an eight- year period. The amount Lee, Inc. is obligated to repay in eight years is $615,650 (rounded to the nearest dollar). a. Assume the interest on Lee, Inc.'s debt is, instead, compounded annually. What amount is the company obligated to repay at the end of the eight-year period? b. What amount is Lee, Inc. obligated to repay in eight years if interest on its $500,000 debt is compounded quarterly? c. What amount is Lee, Inc. obligated to repay in eight years if interest on its $500,000 debt is compounded monthly? 6. Ordinary Annuities - Remember, ordinary annuities are amounts paid at the end of each period. a. Future values 1. Advanced Engineering Group's cash flow forecast indicates that for the next 24 months, the Group will be able to invest $50,000 in cash at an annual interest rate of 6.98% (monthly rate = 6.98%/12). The Group will invest the cash at the end of each month. At the end of 24 months, how much cash will Advanced Engineering Group have accumulated through this investment practice? i. What is the amount that Advanced Engineering Group accumulates if it invests $300,000 every six months for two years at the same annual interest rate (semiannual rate = 6.98%/2)? iii. Advanced Engineering determines that for an extra $5,000 in administrative expense over two years, it could invest $25,000 semimonthly (twice per month) at the same annual interest rate as in part a. (semimonthly rate of 6.98%/24). Does the extra interest earned justify the additional administrative expense? b. Present values I. ABC Corp. wishes to invest a fixed sum at 4.65% and withdraw $12,000 at the end of each month for the next three years. How much ABC will need to invest? In other words, what is the present value of an ordinary annuity of $12,000 for 36 periods, discounted at a rate of 4.65%/12 per period? ii. Assume that ABC Corp can earn 4.65%, but needs to withdraw $12,000 for 72, not 36 months. How much cash must it now invest to meet its $12,000 / month needs? iii. Assume that ABC Corp. can only earn 3.5% on its investment. What sum does it now need to invest to meet its $12,000 / month cash needs for 72 months? 7. Annuities Due - Remember, annuities due are amounts paid at the beginning of each period. Future values 1. You decide to place $200 at the beginning of each month in an investment account earning interest at 4.63% annually (4.63%/ 12 monthly). You plan on following this practice for five years (60 months). How much will you have accumulated in the account at the end of the five-year period? ii. An investor invests $80 in an account that returns 5.2% annually (5.2%/12 per month). How much is the investor's account worth at the end of the five-year period? a. iii. Gorman Corp. is attempting to build its cash reserves. Its CFO has determined that it can invest $40,000 at the beginning of each month in an account earning 6.45% annual interest (6.45% / 12 monthly). How long (in months) will Gorman need to follow this strategy to accumulate $3,000,000? b. Present values 1. Assume you are able to purchase a financial instrument (an annuity) that will pay you $400 on the first day of each month for the next five years. Ignoring any problems of collectability and assuming 7.10% annually (7.10% / 12 monthly) is a proper discount rate, how much should you pay for this financial instrument if you want to purchase it? ii. Using the financial instrument above again, if the discount rate changes to 8.5% annually, what is the new purchase price? ili. An owner of a building wishes to sell his rights to a stream of rental payments due on the first day of each month for the next two years. The monthly payments total $5,000 and the correct annual discount rate is 5.25% (5.25% / 12 per month). How much should the building owner be able to charge for the stream of payments (i.e., for the annuity)? C. Retirement planning (an application of future values) i. Assume you make annual contributions to a Roth IRA of $1,250 per year beginning on your 25th birthday. Assume further that the account is projected to earn an annual return of 6.15% and that you will retire on your 65th birthday. What is the projected balance in the account on the date of your retirement? Assume no contribution on your 65th birthday. In other words, the last contribution occurs at the beginning of the 40th year, on your 64th birthday. ii. Assume you begin making the contributions above on your 35th birthday, rather than your 25th birthday, but double the annual contribution to $2,500. What is the projected balance in the account on the date of your retirement? iii. If you wait until your 40th birthday to begin making contributions, how much do you have to contribute annually, to reach the same projected account balance on your 65th birthday, as if you had begun contributing at age 25? 8. Jim's Discount Warehouse sells three-year extended warrantees on its televisions and other electronics. As of December 31, 2019, Jim's estimates expected cash flows associated with electronics sold to date as follows for the next three years: 2020 Cash Flow Estimate $15,000 20,000 27,000 Probability Assessment 0.25 0.40 0.35 Total Expected Cash Flow $3,750 8,000 9,450 21,200 2021 20,000 22,500 30,000 .35 .35 .30 7,000 7,875 9,000 23,875 2022 30,000 35,000 40,000 .25 .25 .50 7,500 8,750 20,000 36,250 Assume the cash flows will occur at the end of the respective years and that the pure rate of interest, plus the expected inflation rate of annual interest equals 3.8%. Use the expected cash flow technique to value the warranty obligation for Jim's Discount Warehouse. 9. Rent scenarios a. Linda Peddler owns a bicycle factory. She could either rent or buy a machine to increase her factory's production capacity. She can rent the machine for its expected life of 10 years for 120 payments of $2,000, due at the end of each month. The appropriate annual discount rate for the payments is 6.50%. At what price should Ms. Peddler be indifferent between renting and purchasing the machine? b. How does your answer to item a change if the annual discount rate moves to 5.80%? The DLW Group signs a commercial lease for office space. Under the terms of the lease, DLW will pay $10,000 in rent at the beginning of each month for five years. The proper annual discount rate for this stream of payments is 8.80%. What is the present value of DLW's obligation under the lease? d. How does your answer to item c. change if the annual interest rate changes to 10.20%? C