 # Monthly rate =. 0084 / 12 = 7%

Yüklə 462 b.
 tarix 05.10.2018 ölçüsü 462 b. • ## Billy’s Pianos receives a loan of \$180,000 today. The stated annual interest rate is 8.4%, compounded monthly. Payments are monthly, starting one month from today. The loan is amortized over 30 years. • ## If Billy pays an equal amount of principal each month, how much will the first payment be?

• Monthly rate = .0084 / 12 = 0.7%
• Amount of principal paid each month = \$180,000 / 360 = \$500
• Amount of interest accrued in first month = \$180,000 * .007 = \$1,260
• First payment = 500 + 1,260 = \$1,760 • ## If Billy makes equal month payments each month, how much will the first payment be?

• 180,000 = C / .007 * [1 – 1 / (1.007)360]
• 180,000 = 131.262 * C
• C = \$1,371.31 • ## If Billy pays an equal amount of principal each month, how much will the last payment be?

• Principal owed in 359 months = 180,000 / 360 = 500
• Interest owed = 500 * .007 = 3.50
• Last payment = 500 + 3.50 = \$503.50 • ## If Billy makes equal month payments each month, how much will the last payment be?

• Note: equal payments means first = last (so same answer as #2)
• 180,000 = C / .007 * [1 – 1 / (1.007)360]
• 180,000 = 131.262 * C
• C = \$1,371.31 • ## Carly Rae pays \$50,000 to open her dating service. She receives \$2,700 per year in cash flow, starting in two years. Annual discount rate is 5%. What is the profitability index?

• PV of benefits = 2700 / .05 * 1 / 1.05 = 51,429
• PV of costs = 50,000
• PI = 51,429 / 50,000 = 1.029 • ## If the effective annual discount rate is 15%, then what is the effective discount rate for 8 months?

• (1.15)8/12 – 1 = 9.76534% • ## Wolfgang will receive royalty payments of \$500 every year, starting 5 years from today and ending 25 years from today. What is the present value of these payments if the effective annual discount rate is 15%?

• Annuity formula for 21 payments, discounted by 4 years due to 1st payment in year 5
• 500/.15 * [1 – 1 / 1.1521] * 1 / 1.154 = \$1,804.59 • ## If the inflation rate this year is 5% and the nominal interest rate is 15%, then what is the real interest rate?

• (1 + real)(1 + inflation) = (1 + nominal)
• (1 + real)(1.05) = 1.15
• 1 + real = 1.15 / 1.05 = 1.0952381
• Real = 9.52381% • ## If Reba uses discounted cash flows, how many years is the payback period for this investment?

• 50000 = 10000/.09 (1 – 1/1.09T)
• 61111 = (10000/.09)/(1.09T)
• 1.09T = (10000/.09)/61111 = 1.81818
• T = ln(1.81818)/ln(1.09) = 6.93726 ≈ 7 • ## If Reba uses undiscounted cash flows, how many years is the payback period for this investment?

• 50000 / 10000 = 5 • ## Pyotr’s Beauty Products is considering buying a new device. This machine would cost \$8,000 today, and require maintenance costs of \$600 every three years, starting in 2 years and ending in 11 years. The machine lasts 12 years, and the effective annual discount rate is 14%. • ## What is the present value of all costs of the machine over its life?

• Purchase cost today and maintenance costs in years 2, 5, 8, and 11
• 8000 + 600/(1.142) + 600/(1.145) + 600/(1.148) + 600/(1.1411) = \$9,125.61 • ## Pyotr pays \$X per year for five years, starting today. These payments will have the same present value as the answer you got from part (a). Find X.

• X + X/1.14 + X/(1.142) + X/(1.143) + X/(1.144) = 9125.61
• 3.91371 * X = 9125.61
• X = \$2,331.70 • ## A bond has a face value of \$750. It pays a coupon of 10% today, one year from today, and two years from today. Two years from today, the bond matures. If the current selling price of the bond is \$800, what is the yield to maturity (expressed as an effective annual discount rate)? • ## Ignore negative root. r = 0.119716 so r = 11.97%. Or… • ## Ignore negative root. x = 1.1197 so r = 11.97% • ## Michael is taking out a loan of \$1,000,000 today and he will pay \$22,000 per month for the next 10 years (120 payments, starting one month from today). The stated annual interest rate is 24%, compounded monthly. 13 years from today, Michael will make one additional payment to pay off the loan. How much will this payment be? • ## PV of monthly payments:

• 22000/.02 * [1 – 1/(1.02120)] = 997,818.55
• ## PV of payment made in 13 years:

• 1,000,000 – 997,818.55 = 2,181.45
• ## FV of payment made in 13 years:

• 2,181.45 (1.02)12*13 = \$47,904.10 Dostları ilə paylaş:

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