Corporate Finance Chapter 5: Interest Rates

Looking to buy a car and offers a loan with an APR of 6% compounded monthly. A) True rate of interest? B) What is EAR?

A) 06/12=0.5% B) (1+0.005)^12-1=6.17%

Yield Curve

"Plot of a bond's yeilds as a function of its maturitiy date." Risk-free interest rates are used to plot the yeild curve to control for risk; this helps make it a benchmark for other interest rates in the lending market. Term structure is the relationship between interest rates (aka bond yeilds) and different terms (ex. 1 year, 2 year, etc); it is a reflection of the expectations of market participants about future changes in interest rates and their assement of the economy. Primairly used for US government secuirits. - In general, interest rates increase with maturity due to having to pay investor extra due to the risk involved with longer bonds. - Used to judge the overall enviroment of the credit market: 1. Flattening means long term rates are falling in comparison to short term rates, which could have implications for a recession. 2. When short term rates exceed long term rated, its inverted (backwards); this means a recession is likely approaching. The overall outlook for the credit market is weak.

I have been offered a job at Wells with an unusual bonus structure. As long as I stay with them, I will get an extra 70,000 every seven years, starting seven years form now. What is the PV of the incentive if I plan to work for the company for 42 years and earn an intersr rate of 6% (EAR)?

- (1+0.06)^7-1=0.5036 - 42/7=6 - EXcel: PMT(0.5036,6,70000,0)

Bank is offering a 20% interest rate in total for a 2 year deposit. Determine an equivalent discount rate for a period length of six months, one year, and one month

- (1+0.2)^1/4-1 -(1+0.2)^1/2^1

I make monthly discount rates on a car loan. It has quoted APR of 5% (monthly compounding). What percentage of the outstanding principal do I pay in interest each month?

- 5%/12=0.42%

Opportunity cost of capital

Best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted - Ex. A friend offers to borrow 1000 form me today and in return pay me 1,100 a year from now. I find the best alternative option is equally as risky as lending to him. It has an expected return rate of 8%; what should I do? Use rate on excel to find rate of return for the investment from your friend

Converting an APR to an EAR

One interest per compouding period is computed, the equivalnet interest rate for any other time period can be computed. - Formula for EAR to APR conversions: 1 + EAR =(1+APR/m)^m [m=number of compoudning periods] - Examples: For EAR yearly with an APR of 6%, (1+0.06/1)^1. For monthyl: (1+0.06/12)^12-1. For bi-yealr: (1+0.06/2)^2-1 For daily: (1+0.06/365)^365-1

On an inflation map, what does the difference between the inflation line and interest rate line mean?

Real interest rates.

I have invested in a business that proudly reports that it is profitable. My investment of 5000 has produced a profit of 300. Managers think that if I leave the 500 invested with them they can generate 300 per year in profits for perpeturity. I note that other invetment opportunites with similar risk offer 8%. Should I remain invested with them?

300/5000=0.06=6% rate of return. Invest elsewhere!

I graduate from college with 30,000 in student loans. If my interest rate is fixed at 4.66% APR monthly compoudning and I repay the loans over a 10 year period, what will be my monthly payment?

- 4.66%/12=0.38833% - 12 X10=120 - Excel: PMt(0.0038833, 120,-30000,0)=313.23

Inflation: real vs nominal rates

- Nominal: rate at which your money will grow if invested for a certain period - Real: Growth of your purchasing power after adjusting for inflaiton.

Determinants of interest rates: term structure, yield curve, Risk-free interest rates

- Relationship between the investment term and interest rate - A plot of bond yeilds as a funciton of the bond's maturity date - rate at which money can be borrowed or lent without risk for a given period. Used to plot the yeild curve to control for risk

What are interest rates? Effective Annual Rate/Annual percentage rate

- The price of using money. - EAR if multiplied by the amount initally invested gives the TOTAL amount of interest earned at the end of one year. - Ex. EAR of 5% and a $100 investment: 100 X (1 +0.05 )=105 in one year. - By rasisng the interest rate factor [(1+r)] to the approporaite power, we can compute an equivalent EAR for periods longer or shorter than 1 year. 100 X (1+0.005)^2 for two years. 100 X (1+0.005)^1/12 for month. - WE can convert a disocunt rate for r for one period to an equivalent discount rate for n periods using this formula: Equivalent n-period discount rate: (1+r)^n-1. This is important becuase when computing present or future values, you should adjust the discount rate to match the time period of the cash flows.

My bank account pays interest monthly with an effective annual rate of 6%. What amount of interest will you earn each month?If you have no money in the bank today, how much will you need to deposit per month to have 100,000 in 10 years?

0.5% per month. - Since it pays out per month, instead of 10 yearly payments, you'll have 120 monthly payments (12 months per month X 10 years). Equivalent monthly rate of 6% per year will be on calc. by (1.06)^1/12-1. Now use PMT formula with monthly rate and payments in months: PMT(0.004868, 120, 0,100000) - PMT= $615.47

Discount rates and loans: A $30,000 car loan has 6.75% APR for 60 months. What is the monthly payment?

1. Find monthly discount rate: APR/M (compounding periods): 0.0675/12=0.005625 - PMT: (0.005625, 60, -30000 (pv), 0 (fv))=590.5

My law firm is purchasing a telephone system that will last for 4 years. I can purcahse the system for an up-front cost of $150,000 or lease it for $4000 paid at the end of each month. The lease price is offerd for a 48 month lease with no early termination. My firm can borrow an interest rate of 6% APR with monthly compounding. Should I purcahse outright or pay 4000 per month?

I need to figure out the present value of the cash flow, but I first need to find the discount rate that corresponds to a period of one month. So, I need to convert the borrwoing cost of 6% APR with monthly compounding to months:(1+0.06)^1/12-1=0.00487 per month. - Now use PV formula: should equal 170,321. So, you should Pay the up front cost insread.

Annual percentage rates

Most common way interest rates are quoted. Gives amount of simple interest earned in one year (interest without the effects of compounding; so it'll just be interest on the principle). Because of this, it'll typically be less than actual amount of interest you earn. - Because it does not refelct the true amount you earn in one year, it cannot be used as the discount rate. Instead, its used to show actual interest earned each compounding period. - Formula: Interest rate per compounding period: APR/M[# compounding periods per year] - To show the actual amount you earn per year, you must convert it to EAR. Ex. Savings acct. advertised with interest rate of 6% APR with monthly compounding. This means 0.5% per month [the chosen compounidng period] via the interest rate per compoudning period formula: 6%/ 12=0.5%. Because interest compounds each month, you have (1+0.005)^12=.061678 or 6.16% at one each, which is higher than quoted APR due to compounding of interest from month to month during the year. In summary, acutal rate of 0.5% per month can be stated as 6% APR with compounded monthly or EAR of 6.1678% actual rate per year.