1. Present value of an annuity: Transit Insurance Company has made an investment in another company that will guarantee it a cash flow of $37,250 each year for the next five years. If the company uses a discount rate of 15 percent on its investments, what is the present value of this investment? (Round to the nearest dollar.)
2. Present value of an annuity: Herm Edwards has invested in a fund that will provide him a cash flow of $11,700 for the next 20 years. If his opportunity cost is 8.5 percent, what is the present value of this cash flow stream? (Round to the nearest dollar.)
3. Present value of an annuity: Craymore Tech. is expecting cash flows of $67,000 at the end of each year for the next five years. If the firm’s discount rate is 17 percent, what is the present value of this annuity? (Round to the nearest dollar.)
4. Present value of an annuity: You are a manager in a manufacturing facility. A vendor has contacted you to gauge your interest in replacing your maintenance workers with a 3-year outsourced contract for $100,000 due in advance. You expect to save $35,000 per year in payroll as a result. Determine if you should accept the vendor’s proposal if a discount rate of 6 percent is applied.
5. Future value of an annuity: Mathew has started on his first job. He plans to start saving for retirement early. He will invest $5,000 at the end of each year for the next 45 years in a fund that will earn a return of 10 percent. How much will Mathew have at the end of 45 years? (Round to the nearest dollar.)
6. Future value of an annuity: You plan to save $1,250 at the end of each of the next three years to pay for a vacation. If you can invest it at 7 percent, how much will you have at the end of three years? (Round to the nearest dollar.)
7. Future value of an annuity: You are a 22 year old college graduate and have just landed your first professional job. Your new employer sponsors a matching 401(k) plan. Suppose you elect to defer 6% of your bi-weekly salary into your 401(k) which translates to $200, and that your employer will match your contributions. Assume an interest rate of 12% compounded monthly. If you continue to fund your 401(k) bi-weekly at this exact same amount until you reach the age of 65, how much will your portfolio be valued at when you retire?
8. Future value of an annuity: You are a 27 year old student graduating with a Masters Degree. Several years ago, you took a basic finance course as an undergraduate, and as a result opened up an IRA. You just began working for a company that sponsors a 401(k) plan; the company will match your contributions. The IRS will allow you to take your IRA portfolio valued at $20,000 and ‘roll it’ into your 401(k) without penalty; assume you do this. If you elect to defer $400 of your salary per month into the 401(k), and your portfolio earns an average of 11% annually until you reach age 62, how much will you have in your 401(k) portfolio?
9. Computing annuity payment: Trevor Smith wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent annually. How much does he need to save each year, beginning at the end of this year to reach his target? Assume he could earn 8 percent on any investment he makes. (Round to the nearest dollar.)
10. Computing annuity payment: You are a 35 year old continuing education student who has just realized the benefit of starting a 401(k). Suppose your employer sponsors a 401(k) plan and will match your contributions. If you assume an interest rate of 9% compounded monthly on level cash flows and you want to have $1.5 million accumulated in your 401(k) portfolio by the time you’re 62, how much will your personal monthly deferral amounts need to be?
11. Perpetuity: A wealthy individual wants to set up a scholarship at his alma mater. He is willing to invest $500,000 in an account earning 10 percent. What will be the annual scholarship that can be given from this investment? (Round to the nearest dollar.)
12. Growing annuity: Hill Enterprises is expecting tremendous growth from its newest boutique store. Next year the store is expected to bring in net cash flows of $675,000. The company expects its earnings to grow annually at a rate of 13 percent for the next 15 years. What is the present value of this growing annuity if the firm uses a discount rate of 18 percent on its investments? (Round to the nearest dollar.)
13. Effective annual rate: Desire Cosmetics borrowed $152,300 from a bank for three years. If the quoted rate (APR) is 4.5 percent, and the compounding is daily, what is the effective annual rate (EAR)? (Round to one decimal place.)
14. You want to buy a home and will take out a mortgage to do so; you expect to put down 3% (plus closing costs) and finance the rest. If the sell price is $200,000 and you enter into a 30-year, 4% monthly mortgage, how much will your monthly payments be? Build an amortization schedule to prove that your calculation is correct.
15. You need a new car and have budgeted up to $350 per month for your car payment. Assuming a interest rate of 3.5% on a 60-month car loan, what is the approximate sticker price you can afford?
TVM – Annuity In-Class Exercise – C. Smith Page 2