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An investment in manufacturing equipment yields the followingcash flows for 8 years. At the end of the 8th year the equipmentcan be sold for $15,000. Assuming an interest rate of 14%(compounded annually), how much would you be willing to invest inthis manufacturing equipment?

C=? I=2000 I=2000 I=2000 I=2000 I=1000 I=1000 I=1000 I=1000 L=$15,000
0 1 2 3 4 5 6 7 8

C: Cost, I: Income,L: Salvage Value

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Keith Leannon
Keith LeannonLv2
28 Sep 2019

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1.) An investment inmanufacturing equipment yields the following cash flows for 8years. At the end of the 8th year the equipment can be sold for$15,000. Assuming an interest rate of 14% (compounded annually),how much would you be willing to invest in this manufacturingequipment?

C=? I=2000 I=2000 I=2000 I=2000 I=1000 I=1000 I=1000 I=1000 L=$15,000
0 1 2 3 4 5 6 7 8

C:Cost, I: Income, L: SalvageValue

2.) Suppose that thenominal annual interest rate on an investment is 12%. Calculate theeffective interest rate if compounding occurs continuously.

3.)

Assume $50,000 is paidfor an asset in present time that yields annual cash flow of $6,000dollars per year in Years 1 through 10, as shown in the tablebelow. At the end of Year 10 the salvage value of the asset is$40,000. Calculate the rate of return on this investment. (In otherwords, find the value of the interest rate i that makesthe Net Present Value of the investment equal to zero - this isalso called the Internal Rate of Return.)

A hint here is thatyou will need to solve this problem either by trial and error orusing the IRR function in Excel.

C=-$50,000 I=$6000 I=$6000 I=$6000 ... I=$6000 L=$40,000
0 1 2 3 ... 10

CAN SOMEONE LET ME KNOW IF I DID THESE RIGHT?? PLEASE

1. What is the effective rate of interest for an investment paying 18% compounded monthly?

Effective rate of interest= (1+r)^n-1

r= 18% or .18; compounded monthly= 0.18/12

N= no of period ie 12

Effective rate r= (1+.18/12)^12-1

= 0.1956 ie 19.56%

2. If you want to buy a $25,000 car in 5 years, what single amount must you invest now at 10% compounded quarterly to have the money to pay cash?

Fv= PV(1+i)^n

Fv= 25,000 n=5 years so 5*4= 20 periods; r = 10% compounded quarterly ie .10/4

25,000=PV(1+.10/4)^20

25,000= PV (4.10/4)^20

PV= (25,000/1.025)^20

PV=$15,256.77

3. What is the present value of $50,000, 4 years from now at 12% interest compounded monthly?

Fv= Pv (1+r)^n

Fv=50,000; Pv?; n= 4 years compounded monthly ie 48; R= 12% compounded monthly ie .12/12

50,000= PV (1+.12/12)^48

PV=50,000/(1.01)^48

PV=$31,013.02

4. What is the future value of $5,000 in 15 years if you can earn 12% interest compounded semi-annually?

Fv=PV(1+i)^n

Fv=5,000; n=15 years semi annually= 30 periods; I=12% compounded semi annually=.12/2

5,000= PV (1+.12/2)^30

PV=5,000(1.06)^30

PV=$28,717.46

5. What is the future value of $800 deposited annually at 9% interest for 25 years if the deposits are made at the end of the period? And, if the deposits are made at the beginning of the period?

FV(end)= PMT[(1+i)^n-1)/i] (Ordinary annuity)

FV= $800; i=9% or .09; n=25 years

Fv+800[(1+0.09)^25-1)/0.09

FV=$67,760.72

FV=(beginning)= PMT[((1+i)^n-1)/i](1+r)

FV=$800; I=9% or 0.09; n=25 years

FV=800[(1+0.09)^25-1)/0.09)(1+0.09)

FV=$73,859.18

6. Using the information from the previous problem, how much more interest is earned from the annuity due than from the ordinary annuity?

Annuity due= annuity (beginning) - ordinary annuity

=$73,859.18-$67,760.72= $6,098.46

7. How much must be deposited now in order to withdraw $15,000 at the end of each year for 30 years, if interest is 11% compounded annually?

Annuity the end of each year= 15,000

N=30 years; r= 11% compounded annually

To find PV of an annuity of $15,000 @ the end of each of the year

PV= PMT [1-(I+i)^-n/i

PV=15,000[1-(I+0.11)^-30/0.11]

PV= PMT[1-(I+i)^-n/i

=$130,406.89

8. If you want $2,000,000 in your retirement fund in 45 years, and you can earn 14% compounded annually, what will be your annual contribution? How much interest will you earn?

FV= 2,000,000; N= 45 years; i= 14% compounded annually

We have the FV of an annuity – to find the annuity

FV= PMT [(I+i)^n-1)/i]

2,000,000=PMT [((1+0.14)^45-1)/(0.14]

2,000,000= PMT [2590.5648]

PMT=$772.03

9. If you retire with $1,375,000 in your retirement fund and plan to live for 20 years, how much can you withdraw every year if your investment earns 10%?

PV= 1,375,000 n=20 years i=10%

To find annuity given the PV

PV=PMT [1-(1+i)^-n/I]

1,375,000= PMT [1-(1+0.10)^-20/0.10)

PMT(yearly withdrawl) =$161,506.98

10. How much more interest is earned from ordinary annuity payments of $6,000 per year for 25 years if you can increase your rate of interest from 6% to 9%?

PMT=$6,000 per year; n=25 years; i=6% to 9%

Interest at 6%

FV= PMT [((1+r)^25-1)/0.06]

FV= 6,000[((1+0.06)^25-1)/0.06]

=$329,187.07

Interest at 9%

FV=6,000[(91+0.09)25-1)/0.09]

= $508,205.38

More earned interest 9%- 6% = $508,209.38 - $329,187.07 = $179,018.31

Consider the following after-tax cash flows:

n A B

0 -2500 -5000

1-6 2000 2500

7 2000 0

MARR is 10% (compounded annually)

(a) Compute the future worths of the projects at the end of period 7.

(b) Assume that the required service period is seven years and that the company is considering a comparable equipment that has an annual lease expense of $10,000 for period seven (to be paid at the end of year 7), if project B is chosen. This will result in an income of $12,500 at the end of period 7. Which project is the better choice, using present worth as the criteria?

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