HW3_S2023 (1)
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Carnegie Mellon University *
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Course
88223
Subject
Finance
Date
Feb 20, 2024
Type
doc
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3
Uploaded by Littlelies
H
OMEWORK
A
SSIGNMENT
#3
1) Tim is graduating and moving from Pittsburgh, so he agrees to sell his car to his friend
Francis. Tim accumulated a lot of credit card debt as a student, and he intends to use the
money from selling his car to pay down his credit card debt, which has an 8% APR
(interest rate). Francis has a part-time campus job that he has used to pay for his meal
plan, but he can use these earnings to pay for the car and then increase his student loan
amount to pay for his meal plan. His student loan has a 6.5% APR (interest rate). Tim and
Francis are considering whether Francis will pay for the car entirely up front with a single
payment of $3000 now or in two installments of $1500 now and another $1700 one year
from now. What is the NPV of each payment plan for each of them? [20 points] Which
payment plan do you expect they will agree on? [5 points]
2) The Righton Corporation is taking out a loan of $38,000 at 7.8% interest (see table
below). This interest rate is locked in for the life of the loan. They recognize that if/when
they want to take out another loan in the future, the interest rate may change, but they
have no reason to expect it to be higher or lower, and they are confident that the bank
would extend them another loan on similar terms. They are considering three different
possible repayment plans for the current loan.
Under Plan 1, they must pay yearly interest of $2,964 and the entire principal at the end.
Plan 2 is an annuity-type plan where they pay equal payments of $5612.14 every year.
With Plan 3, they pay a balloon payment of principal plus all accumulated interest in year 10. Year
Plan1
Plan2
Plan3
0
38,000
38,000
38,000
1
-2,964
-5612.14
0
2
-2,964
-5612.14
0
3
-2,964
-5612.14
0
4
-2,964
-5612.14
0
5
-2,964
-5612.14
0
6
-2,964
-5612.14
0
7
-2,964
-5612.14
0
8
-2,964
-5612.14
0
9
-2,964
-5612.14
0
10
-40,964
-5612.14
-80,533
payment sum:
-67,640
-56,121.4
-80,533
NPV:
?
?
?
a)
Show how the bank calculates the balloon payment of $80,533. [5 points]
1
b)
What are the NPVs of the payment streams for the three plans? Can you use NPV to recommend one plan over the others? Why should one plan be preferred over another? [10 points]
c)
Suppose that the company agreed on paying the 7.8% rate and signed a contract locking in that rate, and then the very next day the market interest rate dropped to 5.5%. Under which plan would the Righton Corporation be happiest? Under which plan would the bank be happiest? Why? How large would the gain or loss in NPV be for each plan? [20 points]
3) The government is proposing a new program to encourage college students to go into government jobs (teaching and service). The program will help cover the cost of college if you work in the government. With the new program, you would only need to pay back college loans for 10 years, regardless of what you owed. Unfortunately, government salaries are generally lower than those in private industry and pay does not grow as fast.
Base salary government job: $70,000/yr starting after graduation
Base salary private industry job: $90,000/yr starting after graduation
Inflation: 6% annually
Government salary growth: 2% over inflation annually
Private salary growth: 3% over inflation annually
Living expenses: $35,000/yr starting after graduation (inflate after that)
Loan interest rate: 4% annually
Annual loan payments: 25% of (salary minus cost of living)
Years before loan forgiveness, government job: 10
Years before loan forgiveness, private job: 15
Cost of college $59,000 per year for each of four years (no inflation)
Discount rate: 9%
Assume that you are a freshman entering college and that once you start in government or
industry, you stay there for 35 years. Should you consider the new government program? [40 points]
2
Additional problems that you should be able to do (not part of the homework)
1)
HighTech Corp. projects an annual cash flow for one of its divisions as follows:
Year
Cash flow ($M)
0
3
1
0
2
-10
3
2
4
2
5
2
6
2
What is the IRR for this cash stream? Discuss graphically.
2) Currently, you have a credit card payment due of $500 at 18% (annual nominal rate) compounded monthly. What is the effective yearly rate? If you make no payments at all for the next six months, how much will owe?
3)
Assume that it is your 22nd birthday (I know that this is hard for some of you to do).
You decide to start saving for your retirement, which will start at age 66. You are trying
to decide between two different savings plans.
Plan 1: You invest $2,000 a year (starting today) for the next n
years on your birthday.
You then leave the money alone earning interest, withdrawing the entire amount on your
66th birthday. You make a total of n
payments.
Plan 2: You wait n
years before you start to invest the $2,000 a year, but once you start,
you continue to invest the money every year until you turn 66. You make a total of 44-
n
payments.
Assuming you can get a 6% effective annual interest rate for either plan, what must
n
be
so that the two plans result in approximately the same amount available for retirement?
Find the closest whole number for n
.
3
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•
.
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