# Expert Solutions

Question 1
The following cash flow forecast was submitted as part of a proposal for a new product line where the annual cash flows are 4 times the quarterly cash flows. Critique this (below or in a MS Word format) from the perspective of the time value of money. No calculations are expected.
Year                    Average Cash Flow                   Annual Sales
2013                        \$5,000,000                            \$20,000,000
2014                        \$6,250,000                            \$25,000,000
2015                     \$10,000,000                             \$40,000,000
2016                     \$15,000,000                             \$60,000,000
2017                     \$16,000,000                            \$64,000,000
Total                     \$52,250,000                          \$209,000,000
Average               \$10,450,000                            \$41,800,000

Question 2
Bert is ready to retire.  His investments total \$900,000 and he is going to invest this in a fund that earns 4% annual interest compounded annually.
a If Bert withdraws \$45,000 annually, how long will his funds last?
b If Bert withdraws \$45,000 annually, how much will be left in the fund after 10 years.
c What annual rate compounded annually would Bert need to withdraw \$50,000 annually for 25 years?
d If Bert delayed retirement for five years, how much would he have to invest annually in the 4% retirement fund, that presently has \$900,000, to increase the fund to \$1 million?

Question 3
A group of UMUCV students are trying to start a new company and are trying to raise \$1,000,000.  A loan at 8% APR compounded monthly was offered.
a If no payments  are made to pay down the loan until the end of year 5, what will be the size of the loan at that time?
b Assuming only interest is paid for the first 5 years, what would be the annual payment be to pay off the loan in the 20 years thereafter (in years 6-25)?
c How long would it take to pay off the loan if payments are \$250,000 annually staring in the coming year (year 1)?
d How long would it take to pay of the loan if payments are \$75,000 annually staring in the coming year (year 1)?

Question 4
Wealthy Uncle Job has been requested by niece Mary to loan her \$25,000 for her wedding.  Three alternative payback plans are shown below.  Loans 1 and 2 would use equal payments.  Loan 3 would be interest only with the balance paid in full at the end (a balloon payment).
a What payments would Mary have to make for each loan? (payment frequency for each is shown below).
b Uncle Joe will take the funds from an account that earns 6% APR compounded annually.  What percentage loss will he lose for each loan compared to his present investment fund?
Loan 1                         Loan 2                   Loan 3
Effective annual rate          5.125%                    5.000%                   4.875%
Loan length in years                 5                              4                                3
Payment frequency          monthly                    annual                    monthly

Question 5
Bonds issued by Frederick County , Maryland can be purchased today  for \$12,750 with a maturity date 8 years from today that have a 5% coupon paid semi-annually.  The par or face value is \$10,000.  What would the yield to maturity (EAR) be on these bonds.

Question 6
The revenues for Polar Express Manufacturing (PEM) are forecasted to follow an arithmetic gradient starting at \$2,000,000 in the coming year (year 1) and  grow \$500,000 per year thereafter.  Costs are forecasted to follow a geometric gradient using a growth rate of 20% with the cost in year 1 estimated at \$1,500,000 a year.  PEM uses a MARR of 15%.
a Using these revenue and costs forecast, determine PEM’s cash flow (revenues minus costs) for the upcoming 10 years and the present worth of the cash flow.
b What are the implications of this forecast?
c Create a graph that illustrates the situation.

Question 7
The investment committee for the AAAcme Company  has received three project proposals for them to approve or reject.  The forecasted cash flows are shown below.  The required upfront investments for each are shown below.   Note that Project Y would also require an additional investment in the first year of operation.  Which one(s) should be approved using the criteria of Discounted Payback Period.   AAAcme uses a MARR of 12% and requires projects to achieve payback by the end of year 3.
Upfront             Year 1
X                \$80,000
Y                \$35,000            \$16,500
Z              \$135,000

Cash Flow
Year                       X                      Y                  Z
1                       \$20,000         \$20,000         \$25,000
2                       \$40,000         \$40,000         \$30,000
3                      \$80,000          \$50,000         \$60,000
4                      \$50,000          \$50,000       \$100,000
5                      \$30,000          \$50,000       \$150,000

Question 8
Peggy Sue is going to donate her art collection to a museum in ten years.  She also wants to set up a fund over these ten years (from annual funds she receives as part of an inheritance) that will provide \$50,000 annually forever starting at the end of year 11 to support the maintenance of this art collection.
Peggy Sue will open the fund today with a deposit of \$100,000 and make an additional deposit at the end of each year thereafter (for 10 years).  The fund into which she is making her deposits and from which the maintenance funds will be deducted has an APR of 5% compounded monthly.
How much should she put into this fund in each of the upcoming ten years to achieve her plan?

Question 9
A machine vendor is trying to sell a machine to Magnum BioTech, LLC  that uses the latest technology to reduce production costs.  The CEO likes the concept but estimates that it will take a few years to achieve the savings since it will take time to learn and adapt to the new technology.
The volume of sales and thereby revenues from selling the product are not expected to change, so only production costs are the issue, which are shown below for the upcoming four years.
The cost to purchase the new machine would be \$450,000.  If the new machine is purchased, the present machine could be sold for \$250,000 in Year 1.
The CEO asked for a comparison of the new machine versus retaining the present machine (no investment required) by determining the annual worth of each using a MARR of 16%.  Determine this for the CEO.
Operational Costs                 1                           2                       3                   4
New Machine                \$600,000            \$500,000          \$400,000        \$350,000
Retain present              \$550,000             \$550,000          \$550,000        \$550,000

Question 10
Universal Machine , LLC is evaluating three alternative machines labeled “Fast”, “Faster” and “Fastest” where increased speed costs more.    All would do the task but the more expensive ones do it faster.  The increased production achieved by the increased speed can be sold.   The existing slow process is also an alternative and would require an overhaul.  The forecasted Cash Flows for each alternative are  shown below.
Which one should be approved if Internal Rate of Return is the sole criteria and a MARR of 15% is used?
Cash Flow
Project     Machine             0                 1                   2                       3                4                  5
Fastest       (\$450,000)    \$125,000    \$140,000      \$150,000     \$155,000      \$160,000
Faster         (\$250,000)      \$70,000      \$80,000         \$85,000       \$85,000        \$85,000
Fast             (\$125,000)     \$40,000       \$40,000         \$40,000      \$40,000         \$40,000
Existing           (\$25,000)      \$15,000      \$15,000         \$15,000       \$15,000        \$15,000

Assignment 5
Ace Welding Services, Inc. has expanded their machine acquisition to five alternative machines/processes and have altered their MARR and time horizon  The data is shown below.    Recommend a single choice for management that uses the internal rate of return criterion.  Submit your solution in a spreadsheet.
MARR                     15%      EAR
Time Horizon          5          years

Alternatives              Investment            Annual Cash Flow             Salvage value
1                                        \$50,000                    \$18,000                             \$0
2                                      \$250,000                    \$85,000                     \$75,000
3                                      \$350,000                  \$105,000                   \$125,000
4                                      \$600,000                   \$150,000                  \$400,000
5                                      \$800,000                   \$165,000                  \$600,000