Exam 2 computations

Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?

2 N -500 PV 9 I/Y FV = 594.05 1 N -600 PV 9 I/Y FV = 654.00 594.05+654=1248.05

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in 5 years if the interest rate is 8%?

4 N; -100 PV; 8 I/Y; FV = 136.05 N; -300 PV; 8 I/Y FV = 349.92 136.05 + 349.92 = 485.97

You plan to invest $500 at the end of each year for the next 4 years. If the interest rate you can earn is 8% annually, find the present value of this annuity due.

500= PMT, 4=n, 8=I, FV=0, PV = 1656.06

You plan to invest $500 at the end of each year for the next 4 years. If the interest rate you can earn is 8% annually, find the present value of this ordinary annuity.

500= PMT, 4=n, 8=I, FV=0, PV =1656.06 1656.06* (1.08) = 1778.54

A factory costs $400,000. You forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. The discount rate is 12%. Is the factory a good investment? Explain.

C0 = -400,000 C1= 120,000, F1= 1 C2 = 180,000, F2 = 1 C3 = 300,000, F3 =1 I = 12 This exceeds the cost of the factory, so the investment is attractive.

Caterpillar Inc., has identified an investment project with the following cash flows. If the discount rate is 8 percent, what is the future value of these cash flows in Year 4? yr 1 1225 y2 1345 y3 1460 y4 1590

CF 0 = 0 CF 1 = 1125 F1=1 CF2=1345 F2 = 1 CF 3 = 1460 F3 = 1 CF 4 =1590 F4 = 1 NPV = I = 8 Down arrow CPT= 4615.07 .....PV So, PV = 4615.07, N = 4, I/Y = 8, PMT = 0, CPT FV = $6278.76

A car dealer gives you the choice between: Which is the better deal if you could earn 8% on your other investments?? Paying $15,500 for a new car today or, Entering into an installment plan where you pay $8,000 today and $4,000 at the end of each of the next two years.

CF 0 = 8000 CF 1 = 4000 F1 = 2 NPV = I = 8 CPT = 151330.06 Since the PV of Option 2 ($15,133) is less than the PV of Option 1 ($15,500), you are better off going with the installment plan.

Suppose you have taken a student loan of $ 24,000, today . You wish to repay the money in the next 48 years, If the interest rate is 1% then how much do you have to pay per year?

N = 48, I = 1%, PV =- 24000, FV = 0, PMT =$632.01

Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? What is the APR?

N = 60, PV = -10,000, FV = 0, PMT = 207.58, CPT i/Y = 0.7499% APR = 0.7499 * 12 = 8.99 = 9% rounded.

You are looking at two savings accounts in BOA. One pays 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use?

NOM = 5.25, EFF = 0%, C/Y = 365 CPT EFF = 5.39% NOM = 5.25, EFF = 0%, C/Y = 2 CPT EFF = 5.32% daily EAR, since the rate is higher and since this is a savings account.

At the end of each month for the next 25 years you will receive a cashflow of $750. If the APR is 5.8%, compounded semi-annually, then what is the value today

NOM = 5.8%, Eff =0, C/y = 2, so CPT EFF = 5.88 EFF = 5.88, C/Y = 12, CPT NOM = 5.7311 PMT = 750, FV = 0, i/y =5.7311/12 = 0.4776 , N = 25*12 = 300, CPT PV = 119432.30

Calculate the current price of a 6.5 % semi-annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 6%

PMT = (1000*6.5%) / 2 = 32.50, YTM = 6% / 2 = 3%, N = 3*2 = 6 years, FV = 1000 PV: 1013.54

You want to receive $50,000 per year in retirement. If you can earn 7.5% per year and you expect to need the income for 25 years, how much do you need to have in your account at retirement?

PMT = -50000; N = 25; I/Y = 7.5; FV = 0; CPT PV = 557,347

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt?

PMT = 10000, I/y = 4.5, N = 4, PV = 0, CPT FV = 42781.91 Additional Fund needed = 75000-42781.92 =$32,218.09 FV 32218.09, N = 4, I/Y = 4.5, PMT = 0, CPT PV = 270168.84

At the end of each quarter for the next 25 years you will receive a cashflow of $750. If the APR is 5.8%, compounded quarterly, then what is the value today?

PMT = 750, FV = 0, i/y = 5.8/4 , N = 25*4 = , CPT PV = 39464.20

At the end of each year for the next 25 years you will receive a cashflow of $750. If the APR is 5.8% annually then what is the value today?

PMT = 750, N = 25, FV = 0, I/Y = 5.8%, CPT PV = 9772.46

An investor buys a bond at face value of $1,000, a 5-year term and annual payments based on a 10% coupon rate, YTM was 10%. Two years later, she wants to sell the bond. Market rates have changed so that now investors are requiring a 15% yield.

PMT: 100 I/Y: 15 N:3 FV: 1000 PV: 885.84 PMT: 100 I/Y: 10 N:3 FV: 1000 PV: 1000

What is the current price of a 7% coupon bond, paying semi- annually with 3 years to maturity, if market interest rates are 5%? The face value of the bond is $1000.

PMT: 70 N:6 I/Y: 2.5 FV: 1000 PV: 1055.08

Bank of America 10% Annually Wells Fargo 9.97% Semi-annually Citi Group 9.95% Monthly Your Bank 9.93% Daily RIC Bank 9.9% Continuously

PR= 0.1/1=10 EAR=10% PR=0.0997/2 =4.99% EAR=10.22% PR=0.0995/12=0.83: EAR = 10.42% PR=0.0993/365=0.03EAR=10.44% 0.099x2ndex ]-1=1.1044 EAR10.44

Redo as perpetuity due: Find the PV of a perpetuity due if the annual cash flow is $5000 and the interest rate is 15%.

PV = 5000 + 5000/0.15 = $38,333

Find the PV of a regular perpetuity if the annual cash flow is $5000 and the interest rate is 15%

PV = 5000/0.15 = $33,333

You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 5.6 percent, compounded monthly. What will be your monthly payment?

PV = 55000, I/y = 5.6/12 = 0.4667, N = 60 , FV = 0, PMT = 1053.11 1053.11/ ( 1.004667) = 1048.21

An annuity pays $12,000 every year for 5 years with the first payment at the end of Year 4. Given a 13% discount rate, the present value of this annuity is

Step 1: PMT = $12,000; N = 5; I/Y = 13; CPT PV; PV = −$42,206.77 Step 2: FV = −$42,206.77; N = 3; I/Y = 13; CPT PV; PV = $29,251.41

Calculate the current price of a 7 % annual coupon bond, with a $1,000 face value which matures in 3 years. Assume a required return of 10%.

r/y = 10, PMT= $70, t=3, FV = $1000; COMP PV= $925.39

A bond is currently offering an annual coupon of 9% annual coupon and a YTM of 12% per year (compounded annually). What would be the selling price of the bond today if the maturity of the bond is 30 years.

r/y: 12 PMT: 90 N: 30 FV: 1000 PV = 758.34