Investment and Return
1. You are offered a T-note that pays $1,000 in 9 months (or 270 days) for $910. You have $910 in a bank that pays a 5% nominal rate, with 365 daily compounding. You plan to leave the money in the bank if you don’t buy the risk-free T-note.
Which investment should you choose? Use the following all three solution methods to verify your answer. Greatest future wealth: FV
Figure out FV of $910 left in a bank with 9 months, and then compare with T-note’s FV=$1,000
Inputs: N = 270, I/Y =5%/365=0.0137%, PV = -$910, PMT=0
Output: PV= $ 944.29
Cause $1.000 > $944.29, so, I will buy T-note. Greatest wealth today: PV
Figure out PV of T-note, and then compare with its $910 cost
Inputs: N = 270, I/Y = 5%/365=0.0137%, PMT=0, FV=$ 1000
Output: PV= $-963.69
$963.69 > $910, so buy the note to raises my wealth. Highest effective rate of return.
Figure out the EAR% on T-note, and then compare with 5%, which is your opportunity cost of capital:
Inputs: N = 270, PV=-$910, PMT=0, FV= $1000
Output: I/Y= 0.0349%
EAR = EAR%=〖 (1+0.000349)〗^365 – 1 = 0.1358 =13.58%
Cause 13.58% > 5%, so I will buy the T-note.
You want to purchase a house: your maximum monthly payment is $1,600, and you also have a saving of $35,000 as the down payment. You apply for a 30-year fixed mortgage loan with APR 4.49%. What is the maximum house price you can afford to buy?
Inputs: PMT=$1,600 FV=0 N=30*12=360 I/Y=4.49%/12=0.3742%
Output: PV=-$316,133.65
Maximum price=$35,000+$316,133.65=$351,133.65
So, I can afford to pay $351,133.65
1. Five year ago, you invested in a 5% semi-annual coupon bond with a face value $1,000 for $910. Today, at the date of maturity, the bond issuer announces that default occurs with a renegotiation price $950. If you accept the renegotiation price at the date of maturity, what is your realized annual rate of return?
PMT= ($1000*5%)/2= $25
Inputs: N=5*2=10, PMT= 25, PV= -910, FV= 950
Output: I/Y= 3.13%
Annual rate of return = 3.13%*2= 6.26%
So,
Which investment should you choose? Use the following all three solution methods to verify your answer. Greatest future wealth: FV
Figure out FV of $910 left in a bank with 9 months, and then compare with T-note’s FV=$1,000
Inputs: N = 270, I/Y =5%/365=0.0137%, PV = -$910, PMT=0
Output: PV= $ 944.29
Cause $1.000 > $944.29, so, I will buy T-note. Greatest wealth today: PV
Figure out PV of T-note, and then compare with its $910 cost
Inputs: N = 270, I/Y = 5%/365=0.0137%, PMT=0, FV=$ 1000
Output: PV= $-963.69
$963.69 > $910, so buy the note to raises my wealth. Highest effective rate of return.
Figure out the EAR% on T-note, and then compare with 5%, which is your opportunity cost of capital:
Inputs: N = 270, PV=-$910, PMT=0, FV= $1000
Output: I/Y= 0.0349%
EAR = EAR%=〖 (1+0.000349)〗^365 – 1 = 0.1358 =13.58%
Cause 13.58% > 5%, so I will buy the T-note.
You want to purchase a house: your maximum monthly payment is $1,600, and you also have a saving of $35,000 as the down payment. You apply for a 30-year fixed mortgage loan with APR 4.49%. What is the maximum house price you can afford to buy?
Inputs: PMT=$1,600 FV=0 N=30*12=360 I/Y=4.49%/12=0.3742%
Output: PV=-$316,133.65
Maximum price=$35,000+$316,133.65=$351,133.65
So, I can afford to pay $351,133.65
1. Five year ago, you invested in a 5% semi-annual coupon bond with a face value $1,000 for $910. Today, at the date of maturity, the bond issuer announces that default occurs with a renegotiation price $950. If you accept the renegotiation price at the date of maturity, what is your realized annual rate of return?
PMT= ($1000*5%)/2= $25
Inputs: N=5*2=10, PMT= 25, PV= -910, FV= 950
Output: I/Y= 3.13%
Annual rate of return = 3.13%*2= 6.26%
So,