Exercises - TVM and Security Valuation

.docx
School
Royal Melbourne Institute of Technology **We aren't endorsed by this school
Course
BUSM 4129
Subject
Finance
Date
Oct 17, 2023
Pages
4
Uploaded by ChiefBoulder11774 on coursehero.com
Time Value of Money / Discounted Cash Flow Basic Practice Questions Practice Exercises 1. You have $15,000 to invest for 4 years at 8% per annum. What is future value? 2. You need $30,000 in 3 years time. The interest rate is 7% per annum. How much do you need to invest now? 3. You invested $8,967 at 6% per annum and now you have $12,000. For how long has your money been invested? 4. You invested $8,000 for 4 years and now have $9,910.60. What interest rate are you receiving. Questions 1 to 4 are of the type where there is just one initial amount. There are four variables - PV, FV, interest rate and number of periods. If you know any three, you can find the fourth. 5. You will be receiving $1,000 in one year's time, $500 in two year's time and $800 in three years time. What is the present value of this set of cash flows if the appropriate discount rate is 5%? 6. The stated annual rate of interest (Annual percentage rate - APR) for an investment is 5%. The compounding period is monthly. What is the effective annual rate (EAR)? 7. You wish to provide a prize of $500 every year forever and ever. The first prize will be awarded in exactly one year's time. How much do you need to provide now to fund this prize? The appropriate discount rate is 4% per annum. 8. You wish to provide a prize every year for ever and ever. The first prize of $500 will be awarded in exactly one year's time. To provide for inflation you specify that the value of the prize is to grow by 3% every year i.e. the second prize will be $515. How much do you need to provide now to fund this prize? The appropriate discount rate is 4% per annum. 9. You wish to receive $10,000 every year for 5 years. The first payment will be in exactly 1 year's time. The appropriate discount rate is 4%. How much do you need to invest now to receive these cash flows? 10. You take out a mortgage of $200,000 at 8% per annum. You will be making 20 annual equal payments with the first payment in exactly 1 year's time. How much is each payment? 11. What is the present value of an annuity that pays $6,000 every year for 10 years, with the first payment in one year's time? The discount rate is 8%. 12. What is the present value of an annuity that pays $6,000 every year for 10 years, with the first payment today? The discount rate is 8%. 1
13. What is the present value of an annuity that pays $6,000 every year for 10 years, with the first payment two years from today? The discount rate is 8%. 14. What is the value of a perpetuity of $70,000 if the discount rate is 11% and the first payment is in one year's time? 15. What is the value of a perpetuity of $70,000 if the discount rate is 11% and the first payment is today? 16. You are taking out a personal loan for $50,000 at an interest rate of 8% p.a. compounding yearly. You will be making 10 equal yearly payments, with the 1st payment in one year's time. What is the yearly payment? 17. You are taking out a personal loan for $50,000 at an interest rate of 8% p.a. compounding six monthly. You will be making 20 equal payments, with the 1st payment in 6 month's time. What is the six monthly payment? 18. What is the value of a growing perpetuity where the first payment is $500, the growth rate is 2.5% and the discount rate is 4.25%? 19. What is the value of a growing perpetuity where the first payment is $500, the growth rate is 2.5% and the discount rate is 4.25%? 20. You are quoted an interest rate of 16% compounding quarterly. What is the effective interest rate? 21. A project has the following cash flows: Y0 -$5,000 Y1 -$1,000 Y2 +$3,000 Y3 +$4,500 If the discount rate is 5%, what is the NPV? 2
Time Value of Money / Discounted Cash Flow Advanced Practice Questions Practice Exercises 1. John wants to have $25,000 in 3 years' time for a deposit on a house. He has recently won $22,000 in a lottery and would like to travel overseas. If he can invest money at 13%, how much can he afford to spend now on travel? 2. A man can buy a block of land for $17,000 cash or payments of $12,000 now and another $11,500 at the end of 5 years. He can earn 13% if he invests his money. Which plan is better? 3. What is the value now of the right to receive $3,000 per annum at the end of each year for the next 3 years followed by $5,000 per annum received at the end of the next 4 years? Use an interest rate of 9%. 4. A company contributed $1,250 per annum into a fund for 5 years. The fund earned 11% per annum and the interest was compounded yearly. After 5 years the company made no more payments but left its money in the fund. How much would be in the fund at the end of 9 years? 5. What is the future value of $27,300 per annum invested for 11 years at 12%? 6. Your grandfather's family trust has decided to pay you $1200 pre quarter for the 4 years that you will take to complete your degree at RMIT. If a fund can earn 6.8% per annum paid quarterly how much should the trust invest now in the separate account in order that the quarterly payments can be made. 7. John is entitled to the fee simple (ownership) of a property with a current market rental value of $6,000 per annum, in advance, upon the death of Jack. Jack is 63 years old and has a life expectancy of 12 years. John would like possession of the property today. What sum should he offer based on an interest rate of 9.5%? (In advance implies Cash flows occur at the beginning of the period and you have to set your calculator in Beginning Mode. This is Annuity Due). 8. A property is sold for $195,000, a deposit of $50,000 is paid at the date of purchase. Under the contract the outstanding balance is payable by annual instalments over a period of 10 years with interest at the rate of 14%. At the beginning of the fifth year the vendor sells his contract at a price that enables the purchaser of the contract to earn 16.75% on his investment. What amount does the purchaser of the contract pay? 9. How much would you pay for an investment that will return $27,500 for the next 10 years and then $36,000 for the next five years? Use an interest rate of 7.3%. 10. A company has borrowed $250,000 on a mortgage against the assets of the business. The loan is to be repaid by equal annual instalments over the 20-year life of the loan. If the interest rate is 14.25% what is the amount of the instalment? Calculate the interest component of the first, third and fifth instalments. What does the balance owe on the mortgage at the start of the ninth year? 3
Page1of 4
Uploaded by ChiefBoulder11774 on coursehero.com