FIN 350 Midterm Harford WINTER 2019
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University of Washington *
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Course
350
Subject
Finance
Date
Apr 3, 2024
Type
Pages
5
Uploaded by DoctorMoonDonkey41
Assume inflation is 2.4% APR,
NAME__W19 ANSWER KEY ____
compounded monthly
1 of 5
1.
You are choosing between two loans. One charges a real interest rate of 7.3% APR, compounded
annually. The other charges a nominal rate of 9.8% APR, compounded semi
‐
annually. Which has the
lower rate? [6]
You need to get these both on equal footing. The easiest is to convert them both into nominal EAR’s. Since the real rate is annual, you need to convert the inflation rate to annual as well. It is given as 2.4% APR, compounded monthly, which is 0.002% per month, so its annual equivalent is (1+(.002))
12
-1=0.024266. Thus, the annual nominal rate to go with the 7.3% real rate is (1.073)(1.024266)-1=0.0990 The other rate is already a nominal rate, but needs to be converted into an EAR: (1+(.098/2))
2
-1=.1004 Thus, the real rate is lower. 2.
A company makes the following offer: give us ten payments of $100, and then we’ll give you $100 per
year forever! Assume that you make the first payment immediately and then make 9 more at annual
intervals. One year after your last payment, they start paying you (this would be year 10). If your
opportunity cost of capital is 10%, should you accept this deal? [8]
You have to compare the PV of what you give to the PV of what you get. What you give is just an
annuity due. What you get is a deferred perpetuity.
What you give:
𝑷𝑽 ൌ 𝟏𝟎𝟎
𝟏𝟎𝟎
.
𝟏𝟎
ቂ𝟏 െ
𝟏
ሺ𝟏
.
𝟏𝟎ሻ
𝟗
ቃ
=675.90
What you get: the value of the perpetuity in the year before it starts is 100/.10 = 1000. Since it starts in
year 10, that means that its value in year 9 is 1000. Its value today is:
𝑷𝑽 ൌ
𝟏𝟎𝟎𝟎
ሺ𝟏
.
𝟏𝟎ሻ
𝟗
ൌ 𝟒𝟐𝟒
.
𝟏𝟎
Pretty crazy, but it’s a bad deal! The value of the perpetuity is less than what you pay to the company
because it is deferred.
3.
Let’s say you put $100 in an account earning 6% APR, compounded monthly. How long will it take for
the $100 to grow to $500? [4]
6% APR, compounded monthly is .06/12 = 0.005 per month.
500
ln
ln
100
322.69months
ln 1
.005
ln 1
.005
FV
PV
n
Assume inflation is 2.4% APR,
NAME__W19 ANSWER KEY ____
compounded monthly
2 of 5
4.
Assume the following term structure of risk
‐
free interest rates:
6 months
1 year
1.5 years
2 years
2.5 years
1.4%
1.3%
1.2%
1.1%
1.0%
**All rates are quoted as semi
‐
annually compounded APR’s.**
a.
Which would have the higher yield
‐
to
‐
maturity: a 2.5 year STRIP or a 2.5 year 4% coupon Treasury bond?
Explain. [6]
The STRIP only has one cash flow, so its YTM is simply the rate for that maturity: 1%. The coupon bond
has cash flows every 6 months, so it puts weight on all 5 rates. Since all of the other rates are higher
than 1%, the coupon bond will have the higher yield to maturity.
b.
If 1.5
‐
year corporate zero
‐
coupon bonds ($1000 par) with BBB rating have credit spreads of 320 basis
points, what would be the price of such a bond? [5]
320 bp is 3.20%. Adding the spread to the Treasury rate of 1.2% gets us to 4.4%: 𝑃𝑉 ൌ
𝐹𝑉
ሺ
1
𝑟ሻ
ൌ
1000
ቀ
1
. 044
2
ቁ
ଷ
ൌ
936.80
c.
If you think the BBB
‐
rated bonds have a 20% chance of default (payoff=$800), and an 80% chance of
paying as promised, what is your expected return from buying the 1.5 year zero
‐
coupon bond in part (b)?
[6]
Expected CF = (.20)(800)+(.80)(1000) = $960
𝑟 ൌ ൬
960.00
936.80
൰
ଵ
ଷ
െ
1
ൌ
0.00818
ൌ
0.818%
0.818% x 2 = 1.64% APR
Assume inflation is 2.4% APR,
NAME__W19 ANSWER KEY ____
compounded monthly
3 of 5
5.
How are IRR and NPV related and how are they different? [6]
IRR and NPV are based on the same cash flow equation. NPV takes the cash flows and discounts them
using the opportunity cost of capital. IRR takes the cash flows and finds the discount rate that creates
a zero NPV. NPV gives you the dollar value impact of a project on the firm. Loosely speaking, IRR tells
you the annualized average return you would get from taking the project. Thus, both try to tell you
the impact of the project, but one does it in terms of value impact and the other does it in terms of
return.
6.
You have to buy a new copier. The cost of the copier is $2000 now, plus $400 per year in maintenance
costs. The copier will last for 5 years. Alternatively, a local company offers to lease the copier to you and
do the maintenance as well. If your discount rate is 6% per year, what is the most you would be willing
to pay per year to lease the copier (your first lease payment is due in one year)? [8]
This is basically an EAC question. You need to know what the EAC of buying the copier is, so you know the maximum annual cost (lease) you would be willing to pay. First get the total PV of owning the copier and then figure the EAC based on that PV: 0 1 2… 5 2000 400 400… 400
5
5
1
1
$2000
$400
$3684.95
.06
.06 1
.06
3684.95
$874.79
1
1
.06
.06 1
.06
PV
EAC
So 874.79 is the maximum lease payment you would be willing to make.
7.
If you plan to hold a coupon bond until maturity, you know it will be worth exactly $1000 at the end
(when it repays par value). Why would you ever buy a coupon bond selling at a premium? [6]
It doesn’t matter whether a bond is selling at a premium, par or discount. The price it sells at is the
price required so that if you pay that price and receive the cash flows from the bond, you will receive
a rate of return that is the going fair market return at that point in time. In premium bonds, you
receive above average income return (current yield), but you suffer a capital loss when the bond
eventually returns to $1000 par value at maturity. These offset to give you a fair total return.
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Assume inflation is 2.4% APR,
NAME__W19 ANSWER KEY ____
compounded monthly
4 of 5
8.
‐
You want to retire with an amount of money in your retirement account that has the same purchasing
power as $2 million does today. Assume that you will retire 45 years (540 months) from now. You expect
to earn a nominal return of 10.8% APR, compounded monthly, on your retirement savings.
a.
What
real
amount should you invest in your retirement account each month (starting one month
from now)? [8]
Treat this as a real annuity (the cash flows are in real terms, as is the FV). You can first find the PV
of the $2 million using a real discount rate and then solve for the annuity cash flow. The monthly
nominal rate is .108/12=.009. The monthly inflation rate is 0.024/12=.002. The monthly real rate is
1.009/1.002
‐
1 = .00699 (this rate is rounded).
5 0
5
4
40
1
46499.1267
46499.1267
1
,
332.77
.006986
1.006986
139
0
.
200000
1.006986
7354
PV
CF
PMT
b.
What will the
nominal value
of your retirement account be when you retire? [4]
The account will have an amount in it that has the same purchasing power as $2million would
have today. Thus, the account will have $2 million plus 540 months of accumulated inflation: $2
million x (1.002)
540
= 5883010.49
9.
You just purchased a condominium in downtown Seattle by taking out a loan for $500,000. The loan is
for 30 years with monthly payments and has a nominal APR of 4.8%, compounded monthly. If you first
payment is due in one month, what will be your monthly payments? [8]
The monthly rate is .048/12=.004. This is a 360 month annuity with a present value of $500,000.
360
1
500,000
500,000
1
,
2623.37
.004
190.5977
1.004
PMT
PMT
How much of your first payment will go toward interest and how much will go toward principal? [4]
We computed the monthly rate of interest to be 0.004 (0.4%). 500,000 x 0.004 is $2000, so after one
month, you owe $2000 in interest. Thus, of your first payment, $2000 goes to interest and $623.37
goes toward principal.
Assume inflation is 2.4% APR,
NAME__W19 ANSWER KEY ____
compounded monthly
5 of 5
10.
When Amazon first went public, its stock price was $18 per share. Its peak price was 21 years later:
$2040. If you invested at the start, what would your annual return have been (your annual compound
return)? [4]
𝒓 ൌ ൬
𝟐𝟎𝟒𝟎
𝟏𝟖
൰
𝟏
𝟐𝟏
െ 𝟏 ൌ 𝟎
.
𝟐𝟓𝟐𝟔 ൌ 𝟐𝟓
.
𝟐𝟔
%
What would your real return have been? [3]
[(1+nominal)/(1+inflation)]
‐
1 = real
Inflation: 0.024/12 = 0.002 per month:
ሺ𝟏
.
𝟎𝟎𝟐ሻ
𝟏𝟐
െ 𝟏 ൌ 𝟎
.
𝟎𝟐𝟒𝟐𝟔𝟔
ሺ𝟏
.
𝟐𝟓𝟐𝟔ሻ
ሺ𝟏
.
𝟎𝟐𝟒𝟐𝟔𝟔ሻ
െ 𝟏 ൌ 𝟎
.
𝟐𝟐𝟐𝟗𝟔 ൌ 𝟎
.
𝟐𝟑 ൌ 𝟐𝟑
%
11.
Assume unexpected economic news released today causes interest rates to increase. How do current
bond prices change? Explain (in a couple sentences) the economic intuition for this. [6]
Current bond prices decrease. The cash flows of existing bonds do not change. Higher interest rates
mean that the opportunity cost of investing in these existing bonds increases, so their prices decrease.
They are a fixed deal and the return from alternative deals has increased.
12.
You are taking out a business loan for a new warehouse. The loan amount is $500,000 and requires
equal monthly payments for 5 years (60 payments) with the first payment due in 1 month. At the same
time as your last monthly payment, you will make one large payment of $100,000 to finish paying off
the loan. Your interest rate is 6% APR, compounded monthly. What are your monthly payments? [8]
0
1
2
…
59
60
PMT
PMT
…
PMT
PMT+$100,000
The PV of what you give the bank has to equal $500,000. If it weren’t for the $100,000, this would be a
straightforward annuity problem. That’s ok: just deal with the $100,000 first. Take the PV of the
$100,000 and subtract it from the $500,000 you’re borrowing. What’s left over is what you have to
cover with your payments, so what’s left over is the PV of the annuity of your payments.
60
60
100,000
500,000
500,000
74,137.22
425,862.78
1.005
1
1
425,862.78
425,862.78
,
8,233.12
.005
51.72556
.005 1.005
PMT
so PMT
Related Questions
Q5
arrow_forward
Suppose that you have two loan choices with monthly payments
Choice
Loan Amount
Term (years)
Interest Rate
1
$
250,000
30
5%
2
$
220,000
30
4.50%
(a)
What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you
hold the loan for the entire term and there are no origination costs for the two loans?
Incremental Borrowing Cost: $3,254.72
(b)
What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you
hold the loan for only 6 years (72 months) and there are no origination costs for the
two loans?
Incremental Borrowing Cost: $650.94
arrow_forward
2. Problem 5.17 (Effective Interest Rate)
еВook
You borrow $225,000; the annual loan payments are $30,017.40 for 30 years. What interest rate are you being charged? Round your answer to the nearest
whole number.
%
arrow_forward
=
Consider two loans with one-year maturities and identical face values: a(n) 8.4% loan with a 1.03% loan origination fee
and a(n) 8.4% loan with a 4.5% (no-interest) compensating balance requirement. Which loan would have the higher
effective annual rate? Why?
The EAR in the first case is%. (Round to one decimal place.)
er cl
arrow_forward
The bank offers you the following three options to pay back the loan from the previous
question:
I:
To pay the interest of 6.00% annually
II:
To pay an interest of 0.49% monthly
III:
To pay an interest of 1.46% quarterly
Which of these three options would be most beneficial for you?
O All three options would be equally beneficial
Option II
○ Option III
Option I
O Option II and Option III would be equally beneficial
arrow_forward
Please answer fast i give you upvote.
arrow_forward
In cell B12, create a formula using the PMT function to calculate the monthly payments for loan Option A. Use the values in cells B8, B10, and B5 for the Rate, Nper, and Pv arguments, respectively, and do not enter any values for the optional arguments. Copy the formula you created in cell B12 into the range C12:D12.
arrow_forward
write down an answer, without showing any work, you will receive only half credit for that problem if you are correct (anc
rong). The point is that I want to see that you know how to set up each problem.
Question 1
Calculate the effective interest rate for each nominal annual interest rate and compounding frequency shown. Round your
answer to 2 decimal places.
a. 12% Quarterly compounding
b. 7% Semiannual compounding
C. 14% Continuous compounding
Upload Choose a File
Question 2
You are looking at buying a new sorting machine for recycling plastics that
sod
6
11-15od
arrow_forward
5. If this loan had been made on a 10% add-on basis payable in 12
end-of-month installments, that would be the monthly
payments? What is the annual percentage rate? The effective
annual rate? ($45,833.33, 17.97%, 19.53%) E
• How does the cost of costly trade credit generally
compare with the cost of shortterm bank loans?
L Focus
F9
F10
F11
F12
8
9
arrow_forward
What discount rate should a lender charge to earn an interest of 2 1/4 % on a 90-day loan?
Hint:
An interest rate r and discount rate d are said to be equivalent if these two simple rates give the same present value for an amount due in the future. Thus, r = d/(1 - dt) and d = r/(1 + rt)
arrow_forward
Suppose your credit card issuer states that it charges a 19.25% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?
a. 21.04%
b. 19.25%
c. 20.18%
d. 20.68%
e. 20.51%
arrow_forward
which of the following statements are true?
1. there is an inverse relationship between interest rates and future vales
2. the effective annual interest rate (EAR) will be higher than the annual percentage rate (APR) for a loan that compounds interest annually
3. there is an inverse relationship between present value and interest rates
4. all else equal, the more frequent interest in compounded on a loan, the more interest you will have to pay.
arrow_forward
I would appreciate it If you could also explain how to plug this into a financial calculator
arrow_forward
3. Suppose you are considering a PLAM with the following characteristics:
Mortgage Amount = $175,000
30-Year Term
Monthly Payments
Current Real Rate = 5.50 percent
Expected Inflation Rates: EOY1 = 3%, EOY2 = -2%, EOY3 thru EOY30 = 0%
Annual Payment Adjustments
A. What is the APR of this loan?
Answer:
B. What is the effective cost if the loan is repaid at the end of year 2?
Answer:
C. Suppose that, instead of repaying the loan, you continue to make the payments and
your monthly payment in year 4 is 1,043.09. What was the inflation rate for year 3?
Answer:
arrow_forward
ff,2
arrow_forward
3. I can borrow from two different banks. One of them is charging me 6.75% APR compounded monthly and the other one charges me 6.65% APR compounded weekly. What is the effective annual rates for each one and which one should I choose? (Show Work)
arrow_forward
Answer it correctly please. I will rate accordingly. Ty-ped answer only...
arrow_forward
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Related Questions
- Q5arrow_forwardSuppose that you have two loan choices with monthly payments Choice Loan Amount Term (years) Interest Rate 1 $ 250,000 30 5% 2 $ 220,000 30 4.50% (a) What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you hold the loan for the entire term and there are no origination costs for the two loans? Incremental Borrowing Cost: $3,254.72 (b) What is the incremental borrowing cost of $30,000 for loan 1 over loan 2 if you hold the loan for only 6 years (72 months) and there are no origination costs for the two loans? Incremental Borrowing Cost: $650.94arrow_forward2. Problem 5.17 (Effective Interest Rate) еВook You borrow $225,000; the annual loan payments are $30,017.40 for 30 years. What interest rate are you being charged? Round your answer to the nearest whole number. %arrow_forward
- = Consider two loans with one-year maturities and identical face values: a(n) 8.4% loan with a 1.03% loan origination fee and a(n) 8.4% loan with a 4.5% (no-interest) compensating balance requirement. Which loan would have the higher effective annual rate? Why? The EAR in the first case is%. (Round to one decimal place.) er clarrow_forwardThe bank offers you the following three options to pay back the loan from the previous question: I: To pay the interest of 6.00% annually II: To pay an interest of 0.49% monthly III: To pay an interest of 1.46% quarterly Which of these three options would be most beneficial for you? O All three options would be equally beneficial Option II ○ Option III Option I O Option II and Option III would be equally beneficialarrow_forwardPlease answer fast i give you upvote.arrow_forward
- In cell B12, create a formula using the PMT function to calculate the monthly payments for loan Option A. Use the values in cells B8, B10, and B5 for the Rate, Nper, and Pv arguments, respectively, and do not enter any values for the optional arguments. Copy the formula you created in cell B12 into the range C12:D12.arrow_forwardwrite down an answer, without showing any work, you will receive only half credit for that problem if you are correct (anc rong). The point is that I want to see that you know how to set up each problem. Question 1 Calculate the effective interest rate for each nominal annual interest rate and compounding frequency shown. Round your answer to 2 decimal places. a. 12% Quarterly compounding b. 7% Semiannual compounding C. 14% Continuous compounding Upload Choose a File Question 2 You are looking at buying a new sorting machine for recycling plastics that sod 6 11-15odarrow_forward5. If this loan had been made on a 10% add-on basis payable in 12 end-of-month installments, that would be the monthly payments? What is the annual percentage rate? The effective annual rate? ($45,833.33, 17.97%, 19.53%) E • How does the cost of costly trade credit generally compare with the cost of shortterm bank loans? L Focus F9 F10 F11 F12 8 9arrow_forward
- What discount rate should a lender charge to earn an interest of 2 1/4 % on a 90-day loan? Hint: An interest rate r and discount rate d are said to be equivalent if these two simple rates give the same present value for an amount due in the future. Thus, r = d/(1 - dt) and d = r/(1 + rt)arrow_forwardSuppose your credit card issuer states that it charges a 19.25% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate? a. 21.04% b. 19.25% c. 20.18% d. 20.68% e. 20.51%arrow_forwardwhich of the following statements are true? 1. there is an inverse relationship between interest rates and future vales 2. the effective annual interest rate (EAR) will be higher than the annual percentage rate (APR) for a loan that compounds interest annually 3. there is an inverse relationship between present value and interest rates 4. all else equal, the more frequent interest in compounded on a loan, the more interest you will have to pay.arrow_forward
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