Econ 134 A Test 1

Fall 2015

Based on Form A

Q1 A stated annual interest rate of 12%, compounded continuously, is equivalent to a stated annual interest rate of %, compounded seven times per year.

Q2

Christina will receive a 10-payment annuity. The first payment will be made 7 years from today, and each subsequent payment will be made yearly until all 10 payments are given to her. The first payment will be $500, and each subsequent payment will be 6% higher than the previous payment. If her effective annual discount rate is 13%, what is the total present value of all 10 payments?

Q2 10-payment annuity; yearly payment; 1st payment @ t=7; 1st payment = $500; g=6%; EAR=13%. PV=?

Q3

A machine requires a $1,000 purchase price today. It lasts for 5 years and has a single maintenance cost of $300 three years from today. What is the equivalent annual cost for this machine if the effective interest rate is 6%?

Q3 Costs: $1,000 @ t=1; $300 @t=3 Lifespan of the investment: 5 years EAR=6%EAC=?

Q4

Luther will receive 3 payments. Each payment will be $100 and paid every six months. The first payment will be made six months from today. The stated annual interest rate is 18% and is compounded monthly. What is the total present value of the 3 payments?

Q4 3 payments of $100; every six months, starting six months from today; SAIR=18%, compounded monthly;PV=?

Q5

Austin will invest $2,000 today. He will receive a payment of $500 one year from today. He will receive subsequent payments annually forever, each 8% lower than the previous royalty payment. If Austin’s effective annual interest rate is 14%, what is the profitability index of this investment?

Q5 Initial cost=$2,000; Perpetuity, annually, starting $500 in a year; g=-8%; EAR=14%.PI=?

Q6

Missy will be receiving a $100,000 loan from the Elliott Song National Bank today. The loan will last for 20 years, but the loan has a 25-year amortization schedule. The effective annual interest rate is 20%. The regular payments will be made yearly, starting one year from today. How much will the balloon payment have to be 20 years from today in order to completely pay back the loan?

Q6 Loan: PV=$100,000; 25-year amortization; annually; starting next year; EAR=20%.

Ending balance @ t=20?

PV of 1st 20 payments:

Q6 Loan: PV=$100,000; 25-year amortization; annually; starting next year; EAR=20%.

Ending balance @ t=20?

PV of balloon payment:

FV of balloon payment:

Q7

Mary needs to figure out which of two mutually exclusive businesses should be located: Business 1 would require $1 million to be invested today, with $150,000 in revenue generated every year, starting one year from today;Business 2 would require $2 million to be invested today, with $250,000 in revenue generated every year, starting one year from today. If the EAR=9%, which should she invest in?

Q7 Offer 1: $150,000 perpetuity with a price of $1 million; Offer 2: $250,000 perpetuity with a price of $2 million; EAR=9%;

NPV1 >=< NPV2 ?