Question

1. Assume that Hamilton Museum knows that the most that it can earn is 5.2%, compounded annually. How long (in years) will it take its $450,000 investment to grow to $675,000? Round your answer to the nearest whole number (e.g. 2 years).
2. Jefferson Company reprints old manuscripts. They could either rent or buy a machine to increase their factory’s production capacity. They can rent the machine for its expected life of 15 years for 180 payments of $1,500, due at the beginning of each month. The appropriate annual discount rate for the payments is 5.6%. At what purchase price should Jefferson be indifferent between renting or purchasing the machine?
3. Adams, Inc. issues a series of $100,000 bonds on January 1, 2020. The bonds pay interest semiannually on July 1 and January 1 of each year at the rate of 4% per year and mature in 10 years. If investors decide that 3.6% per year is an appropriate interest rate for the Adams bonds, how much will they be willing to pay for each bond?
4. The Hamilton Museum would like to invest $450,000 now in order to have $675,000 available 5 years, at which time it hopes to build a new wing on the museum. At what interest rate, compounded annually, would the museum need to invest the funds to achieve this goal? (Round your answer to the nearest tenth of a decimal, e.g. 3.5%.)
5. Washington Corporation is attempting to determine whether to purchase a new machine for its factory. The initial cost of the machine is $2,500,000. The company intends to pay cash for the machine. The firm estimates that the machine will generate cash flows, net of operating costs, of $750,000 for the first two years and $500,000 per year in years three through five. The machine is expected to last for five years and will have no value at the end of its useful live (i.e. no salvage value). The firm uses a 6.4% annual rate to discount its cash flows. Assume the cost of the machine is incurred at the beginning of the first period (1/1/2019) and the cash inflows generated by the machine are received at the end of the first (12/31/2019) through fifth (12/31/2023) years of the machine’s useful life. Should the firm purchase the machine? Support your answer with calculations.

Answer 1

1)How long (in years) will it take its $450,000 investment to grow to $675,000?

Formula for Compound Interest

A=P(1+r/n)^nt

where,

A=Amount

P=Principal

r=Interest rate

n=number of times interest is compounded per year

t=time (years)

=675000=450000(1+0.052/1)^1*t

=675000/450000=(1.052)^t

Using log on both sides

ln (1.5)=ln (1.052)^t

t=ln (1.5)/ ln (1.052)

t=0.405465/0.050693

t=8 Years

2)At what purchase price should Jefferson be indifferent between renting or purchasing the machine?

For Jefferson to be indifferent purchase price should be equal to present value of rent payments for 180 months calculated at the discount rate of 0.47% (5.6%/12).

=Sum of Cash Flow * Sum of Present Value Factor @ 0.47%

=$3191.49

Present Value factor= 1/(1+0.47)^n

where n =number of month (which is to be calculated for each month.

Sum of Cash Flow= 1500*180=270000

3)how much will they be willing to pay for each bond?

They will be willing to pay value equal to current price of the bond which is calculated as given below

Years ( Semi Annually) (10*2)	Cash Flow (100000*2%)	Present value Factor @1.8% (3.6%/2)	Present Value
1	2000	0.965	1930.50
2	2000	0.932	1863.42
3	2000	0.899	1798.67
4	2000	0.868	1736.16
5	2000	0.838	1675.83
6	2000	0.809	1617.60
7	2000	0.781	1561.39
8	2000	0.754	1507.13
9	2000	0.727	1454.76
10	2000	0.702	1404.21
11	2000	0.678	1355.42
12	2000	0.654	1308.32
13	2000	0.631	1262.85
14	2000	0.609	1218.97
15	2000	0.588	1176.61
16	2000	0.568	1135.73
17	2000	0.548	1096.26
18	2000	0.529	1058.17
19	2000	0.511	1021.40
20	2000	0.493	985.90
Price of the Bond	16549.69

4)At what interest rate, compounded annually, would the museum need to invest the funds to achieve this goal?

Formula for Compound Interest

A=P(1+r/n)^nt

where,

A=Amount

P=Principal

r=Interest rate

n=number of times interest is compounded per year

t=time (years)

675000=450000(1+r/1)^1*5

675000/450000=(1+r)^5

(1+r)=(1.5)^1/5

Solving using bad power formula

(1+r)=1.0845

r=0.845=8.45%

Note:Bad Power Formula Steps

Step-1 =Sqrt 1.5 tweeleve times on calculator

Step-2= Subtract 1 from the value derived above

Step-3=Divide it by 5 i.e year of compunding

Step-4= Add 1 in the value derived above

Step-5= Press *= tweleve times on calculator to arrive at 1.0845

5)Should the firm purchase the machine?

As the NPV is positive i.e. 39251.26 the machine should be purchased.

Calculation of NPV

Years	Cash Flow	Present value Factor @ 6.4%	Present Value (Cash Flow* Present Value factor)
0	-2500000	1.000	-2500000.00
1	750000	0.940	704887.22
2	750000	0.883	662487.99
3	500000	0.830	415092.72
4	500000	0.780	390124.74
5	500000	0.733	366658.59
Net Present Value	39251.26