Computer Modelling in Finance: Homework 1 2023 Business & Finance
2023 Problem 1 4 You plan to start saving for your son s university education He will begin university when he
Problem 1 (4%)
You plan to start saving for your son’s university education. He will begin university when he turns 18 years old and will need $4,000 then and in each of the following three years. You will make a deposit at the end of this year in an account that pays 6 % compounded annually, and an identical deposit at the end of each year, with the last deposit occurring when he turns 18. If an annual deposit of $1,484 will allow you to reach your goal, how old is your son now?
Problem 2 (2%)
Assume that you deposit $10,000 today into an account paying 6% annual interest and leave it on deposit for exactly 8 years.
How much will be in the account at the end of 8 years in interest is compounded semi-annually?
Problem 3 (4%)
Imagine that you are a professional personal financial planner and one of your clients has asked you the following two questions. Use the time-value-of-money techniques to develop appropriate responses to each question.
a. I need to save $37,000 over the next 15 years to fund my 3-year-old daughter’s college education. If I made equal annual end-of-year deposits into an account that earns 7% annual interest, how large must this deposit be?
b. I borrowed $75,000 and am required to repay it in 6 equal (annual) end-of-year installments of $3,344 and want to know what interest am I paying?
Problem 4 (4%)
An Indiana state savings bond can be converted to $100 at maturity six years from purchase. If the state bonds are to be competitive with U.S. savings bonds, which pay 8 percent annual interest (compounded annually), at what price must the state sell its bonds? Ignore taxes and assume no cash payments on savings bonds prior to redemption?
Problem 5 (4%)
To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $220,000 by the end of 42 years from today. You plan to make equal annual end-of-year deposits into an account paying 8 percent annual interest.
a. How large must the annual deposits be to create the $220,000 fund by the end of 42 years?
b. If you can afford to deposit only $600 per year into the account, how much will you have accumulated by the end of the forty-second year?
Problem 6 (4%)
Find the present value of a 3-year, $20,000 ordinary annuity deposited into an account that pays 12 percent interest, compounded monthly. Solve for the present value of the annuity in the following ways:
a. As three single cash flows discounted at the stated rate of interest
b. As three single cash flows discounted at the appropriate effective rate of interest
c. As a 3-year annuity discounted at the effective rate of interest
Problem 7 (2%)
Determine the annual payment required to fund a future annual annuity of $12,000 per year. You will fund this future liability over the next five years, with the first payment to occur one year from today. The future $12,000 liability will last for four years, with the first payment to occur seven years from today. If you can earn 8% on this account, how much will you have to deposit each year over the next five years to fund the future liability?
Problem 8 (4%)
You are planning to purchase a caravan for $40,000, and you have $10,000 to apply as a down payment. You may borrow the remainder under the following terms: a 10-year loan with semiannual repayments and a stated interest rate of 6 %. You intend to make $6,000 payments, applying the excess over your required payment to the reduction of the principal balance.
a. Given these terms, how long (in years) will it take you to fully repay your loan?
b. What will be your total interest cost?
c. What would your interest cost be if you made no prepayments and repaid your loan by strictly adhering to the terms of the loan?
Problem 9 (4%)
The AutoSave Company buys a machine for $25,000 and expects a return of $2,385.21 per year for the next ten years. What is the expected rate of return on the machine?
Problem 10 (4%)
You decide that your family would be comfortable living on an annual income of $150,000, growing at 4% per year. You’d also like to continue generating this cash flow for your descendants, forever. With investment returns of 8%, how much wealth would you need today to provide this income starting with $150,000 one year from now?
Problem 11 (4%)
Your friend Anna owns a fashion shop in Hamilton, which is currently in financial crisis. She offers you an opportunity to invest $40,000 in the shop on 28/12/2009, and guarantee you cash back at the date and amount stated as below. If your expected rate of return is 12%, what will be the Net Present Value of this investment? What is the Internal Rate of Return?
Date |
Cash Flow |
1/1/2010 |
$14,000 |
3/2/2010 |
$15,593 |
12/29/2010 |
$11,234 |
1/1/2011 |
$3,456 |
8/12/2011 |
$2,345 |
12/19/2011 |
$12,459 |
5/5/2012 |
$1,598 |
Problem 12 (4%)
Mary Chong, capital expenditure manager for PDA Manufacturing, knows that her company is facing a series of monthly expenses associated with installation and calibration of new production equipment. The company has $1 million in a bank account right now that it can draw on to meet these expenses. Funds in this account earn 6% interest annually, with monthly compounding. Ms Chong is preparing a budget that will require the company to make equal monthly deposits into their bank account, starting next month, to ensure that they can pay the repair costs they anticipate over the next 24 months (shown as follows). How much should the monthly bank deposit be?
Months Repair Costs per Month 1–4 $100,000 5–12 $200,000 13–24 $500,000
Problem 13 (4%)
A loan of $80,000 will be repaid in 10 half-yearly installments. If the annual interest rate is 10%, what is the amount of each required half-yearly payment?
Problem 14 (4%)
CEPR records the following cash flows at the end of each year for a project. If the firm’s discount rate is 11%, what is the value of the project at the end of the last year?
Year |
Cash flow |
1 |
$894,633 |
2 |
$542,149 |
3 |
$836,200 |
4 |
$706,080 |
5 |
$520,354 |
Problem 15 (4%)
In five years, you plan on starting graduate school to earn your MBA. You know that graduate school can be expensive and you expect you will need $15,000 per year for tuition and other school expenses. These payments will be made at the BEGINNING of the school year. To have enough money to attend graduate school, you decide to start saving TODAY by investing in a money market fund that pays 4% APR with monthly compounding. You will make monthly deposits into the account starting TODAY for the next five years. How much will you need to deposit each month to have enough savings for graduate school? (Assume that money that is not withdrawn remains in the account during graduate school and the MBA will take two years to complete).
Problem 16 (9%)
Casino.com Corporation is building a $25 million office building in Adelaide and is financing the construction at an 80 % loan-to-value ratio, where the loan is in the amount of $20,000,000. This loan has a ten-year maturity, calls for monthly payments, and is contracted at an interest rate of 8%.
Using the above information, answer the following questions:
1. What is the monthly payment?
2. How much of the first payment is interest?
3. How much of the first payment is principal?
4. How much will Casino.com Corporation owe on this loan after making monthly payments for three years (the amount owed immediately after the thirty-sixth payment)?
5. Should this loan be refinanced after three years with a new seven-year 7 per cent loan, if the cost to refinance is $250,000? To make this decision, calculate the new loan payments and then the present value of the difference in the loan payments.
6. Returning to the original ten-year 8 per cent loan, how much is the loan payment if these payments are scheduled for quarterly rather than monthly payments?
7. For this loan with quarterly payments, how much will Casino.com Corporation owe on this loan after making quarterly payments for three years (the amount owed immediately after the twelfth payment)?
8. What is the annual percentage rate on the original ten-year 8 % loan?
9. What is the effective annual rate (EAR) on the original ten-year 8 % loan?
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