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Interest rate per compound period=APR/M(# Compounding period per year)Effective interest rate= (1+.07/12)^12 – 1 = 7.23% ..A bank offers a loan that will require you to pay 7% interest compounded monthly. Which of the following is closest to the EAR charged by the bank? Q. Your bank is offering you a 30-year fixed mortgage with an EAR of 10% compounded monthly. If you plan to borrow $200,000, what will be your monthly payment? Solution: This is a two part problem. You first need to go from EAR to APR to find the interest rate and then use the annuity formula to solve for the payment. The APR rate is 1 + 0.10 = (1 + AP R/12)^12 ⇒ AP R = 9.56%, then the monthly interest rate is 0.0956/12 = 0.00797. For the payment, solve 200000 = Payment / 0.00797 × ( 1 – 1/ (1 + 0.00797)^360 ) ⇒ Payment = 1691.78 Formula: 1+EAR = (1+ APR/M)^M OR EAR= (1+APR/M)^M -1 EX:#2 Your bank is offering you a 30 yr mortgage w/ an EAR of 6.8% if you plan to borrow 150,000 what will your monthly payment be? -Formula: for pv of annuity – PV= C/R X ( 1- (1/1+R)^N Step1 EAR= 6.8% Has to be converted by 1+ EAR = ( 1 + APR/12 )^12=

… [1.068^1/12-1]x12 =APR

= 1.005-1=.005X12 = R=.066% ……THEN .066/12=.0055 = 150,000 = C/(.066/12) X (1 – (1/1+.066/12)^360 ) = 957 or find C by 150,000 x .0055 / (1 – (1/1.0055)^360 …360 bc 30 yrs x 12 montly Formula:1 +Real interest rate=1+nominal rate/1+inflation rate EX. 1 + Real Interest Rate = 1+0.0975/ 1+0.0375 ⇒ Real Interest Rate = 5.78% Formula: Bond Value = C/R X ( 1- ( 1/(1+R))^N + FV/(1+R)^N

N=# OF PERIODS

Formula: PV= FV/(1+R)^N FOR ZERO COUPON BOND WHICH R =(cost of capital/discount rate/inters rate) Formula: Coupon = (coupon rate x par value / frequency ) Formula: year to maturity = PRICE = C/YTM X (1 – (1/1+YTM)^N) + FV/(1+YTM)^N On exam you plug in the answers of year to maturity and make sure it’s the same frequency EX: 15%/2 IF SEMI plugs into EX. 800 = 25/ r ×( 1 – (1/ (1 + r)^ 10 ) + 1000 / (1 + r)^ 10 To find 25 by taking the COUPON 5%=.05/2 which equals . 025x1000 face value = 25 THIS ONE IS ALSO HOW TO FIND PRICE Formula: Consider (3) – 30 yr. bond w/ annual coupon payment, 1 bond at 10% , 5%, and 3 % Coupon rate. if YTM is 5% what is the price of each bond per 100 face value? 10% x 100/frequency(1) to find the numerator = 10 OR COUPON RATE X FACE VALUE/FREQUENCY P= 10/5% x (1 – ( 1/ 1+.05)^30 + (100/1.05)^30 = 176.86 …… .05 is the YTM of 5% BUT DEPENDS ON FREQUENCY *bonds with long term are more sensitive to changes in interest rates Formula: PV=C/R for bonds that pay coupon payments but never mature PV= DIV/Re-G Similar to growing perpetuity (Future Profitable at time 1) ex: a dividend paid .50 at time 0 and increase by 2% per year. RO IS 15% how much would the stock be? Po= .50 (1+.02) / (.15-.02)= 3.92 Formula for growing perpetuity= Po= DIV1/RE-G Solve for G EX. Microsoft share at 94.64 and annual dividend is 1.56 and equity cost of capital is 8% what is the growth rate? 94.64 = 1.56/.089-G ; G= - 1.56/ 94.64 + .089 ; G=7.25% Microsoft Corp. will pay a dividend of $1.56 one year from today. It is expected that Microsoft will experience a period of very rapid growth in which their dividend will grow by 20% for years 2 through 4. Thereafter its dividend will grow only by 2% (the dividend at time 5 is 1.02 times the one at time 4). If Microsoft’s equity cost of capital is 5%, what should be the price of a share of Microsoft today? This is a two part problem where the first part is for the fast growth rate of 20% and the second part is for the slow growth of 2%. Answer P = 1.56/ 0.05 − 0.20 × ( 1 – ( 1 + 0.20/ 1 + 0.05 )^4 +( 1.56 × 1.20^3 × 1.02)/ 0.05 − 0.02 ÷ 1.05^4

growing annuity

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How to find g? g = R.R X ROE FOR G WILL GO TO THE PO=DIV1/RE-G EX G=.1248 X .2937 = 3.66% Z Inc. is expected to pay a $3.00 dividend at the end of this year (this is year 1). If you expect Z Inc’s dividend to grow by 6% per year forever and their equity cost of capital to be 13%, what is the price of one share? Use the growing perpetuity formula, Price = 3/ 0.13−0.06 = 42.86 or PV=C/R-G (After finding price) The price at time 0 is the above price discounted back two periods, Price t=0 = 1055.08 / (1+0.025)4 = $955.85~ Discount again by answer/ (1+apr/frequency)^N to get to time 0 16. ABC Corp. has a share price of $10 today. In one year, it is expected ABC Corp. will pay dividend of $0.50 and its stock price is expected to be $12. What is ABC Corp.’s equity cost of capital? 10 = 12+0.5/ 1+rE ⇒ rE = 25%...