You invest $50,000 now and receive $10,000 per year for 15 years starting at the end...

You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the discounted payback period? Use i = 9% annual rate compounded annually. Give the discounted payback period between two consecutive integers.

Expert Solution

investment of 50000 and return of 10000 every year for 15 years

i = 9%

We need to find net present value of each cash flow and then find cumulative cash flow

We need to find year when cumulative cash flow turns positive

using excel

Year	Investment	Return	Discount factor	Present Value	Cumulative cash flow
0	-50000		1.000000	-50,000.00	-50,000.00
1		10,000.00	0.917431	9,174.31	-40,825.69
2		10,000.00	0.841680	8,416.80	-32,408.89
3		10,000.00	0.772183	7,721.83	-24,687.05
4		10,000.00	0.708425	7,084.25	-17,602.80
5		10,000.00	0.649931	6,499.31	-11,103.49
6		10,000.00	0.596267	5,962.67	-5,140.81
7		10,000.00	0.547034	5,470.34	329.53
8		10,000.00	0.501866	5,018.66	5,348.19
9		10,000.00	0.460428	4,604.28	9,952.47
10		10,000.00	0.422411	4,224.11	14,176.58
11		10,000.00	0.387533	3,875.33	18,051.91
12		10,000.00	0.355535	3,555.35	21,607.25
13		10,000.00	0.326179	3,261.79	24,869.04
14		10,000.00	0.299246	2,992.46	27,861.50
15		10,000.00	0.274538	2,745.38	30,606.88

Cumulative cash flow turns positive in 7th year

Discounted pay back period = year bef cash flow turns positive + (cumulative cash flow in year bef the positive value/net present worth of cash flow in the year where cumulative cash flow turn positive)

= 6+(5,140.81/5470.34)

= 6+ 0.93976

= 6.939 years = 6.94 years

Showing formula in excel

Year	Investment	Return	Discount factor	Pressent Value	Cumulative cash flow
0	-50000		=1/((1+0.09)^A19)	=B19	=E19
1		10000	=1/((1+0.09)^A20)	=C20*D20	=E20+F19
2		10000	=1/((1+0.09)^A21)	=C21*D21	=E21+F20
3		10000	=1/((1+0.09)^A22)	=C22*D22	=E22+F21
4		10000	=1/((1+0.09)^A23)	=C23*D23	=E23+F22
5		10000	=1/((1+0.09)^A24)	=C24*D24	=E24+F23
6		10000	=1/((1+0.09)^A25)	=C25*D25	=E25+F24
7		10000	=1/((1+0.09)^A26)	=C26*D26	=E26+F25
8		10000	=1/((1+0.09)^A27)	=C27*D27	=E27+F26
9		10000	=1/((1+0.09)^A28)	=C28*D28	=E28+F27
10		10000	=1/((1+0.09)^A29)	=C29*D29	=E29+F28
11		10000	=1/((1+0.09)^A30)	=C30*D30	=E30+F29
12		10000	=1/((1+0.09)^A31)	=C31*D31	=E31+F30
13		10000	=1/((1+0.09)^A32)	=C32*D32	=E32+F31
14		10000	=1/((1+0.09)^A33)	=C33*D33	=E33+F32
15		10000	=1/((1+0.09)^A34)	=C34*D34	=E34+F33

Rahul Sunny answered 2 years ago

1) You invest $50,000 now and receive $10,000 per year for 15 years starting at the...

1) You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 9% annual rate compounded annually, and use the discounted payback approach (not Simple Payback).

You are investing for retirement starting at age 25. You invest $10,000 per year. During years...

You are investing for retirement starting at age 25. You invest $10,000 per year. During years 1-30 your investments earn 15% per year. During years 31-40 you move to more conservative estimates earning 5% per year. How much will you have saved when you retire at age 65? Assume investments occur at the beginning of each year. What is the IRR of this investment stream? (answer is IRR=11.9%) In excel functions

32. You just won a contest! You will receive $50,000 a year for 30 years, starting...

32. You just won a contest! You will receive $50,000 a year for 30 years, starting today. If you can earn 10 percent on your investments, what are your winnings worth today? A. $150,000.00 B. $333,333.33 C. $436,510.50 D. $450,000.00 E. $518,480.30 33. A local magazine is offering a $10,000 grand prize to one lucky winner. The prize will be paid in five annual payments of $2,000 each, starting one year after the drawing. How much would this prize be...

You just won a contest! You will receive $50,000 a year for 30 years, starting today....

You just won a contest! You will receive $50,000 a year for 30 years, starting today. If you can earn 10 percent on your investments, what are your winnings worth today? A. $150,000.00 B. $333,333.33 C. $436,510.50 D. $450,000.00 E. $518,480.30

question 1 "You invest $4,600 now and receive $2,000 at the end of year 1, $1,800...

question 1 "You invest $4,600 now and receive $2,000 at the end of year 1, $1,800 at the end of year 2, $1,600 at the end of year 3, and so on. In what year do you break even on your investment? Use the discounted payback approach and assume an annual interest rate of 4.2%, compounded annually. Enter your answer as an integer."

You are to receive an end-of-year bonus of $50,000 increasing by $1000 for each of the...

You are to receive an end-of-year bonus of $50,000 increasing by $1000 for each of the next ten years. If MARR is 12% and inflation rate is anticipated to be 2%, what will be purchasing power?

Suppose you are going to receive $10,000 per year for 6 years. The appropriate interest rate...

Suppose you are going to receive $10,000 per year for 6 years. The appropriate interest rate is 11 percent. a. What is the present value of the payments if they are in the form of an ordinary annuity? b. What is the present value if the payments are an annuity due?

Assume that you pay $10,000 to receive $2,000 per year in years 1 through 5. $3,000...

Assume that you pay $10,000 to receive $2,000 per year in years 1 through 5. $3,000 per years in years 6 through 8, and $4,000 in year 9, with cash flows to be received at the end of the year. If you require a 14% rate of return, what is the NPV of these cash flows? PLEASE EXPLAIN HOW TO DO THIS WITH A FINANCIAL CALCULATOR NOT THE FORMULA Step by step. Please give small details that you may think...

Would you rather receive: $5,500 at the end of three years, $1,200 per year for 7...

Would you rather receive: $5,500 at the end of three years, $1,200 per year for 7 years or $750 per year for 15 years if the discount rate is 20%? 5a) Would your answer change if discount rate is 2%? If the answer does change, explain in a simple sentence “why”/what happened?

How much money do you need to invest now, to have $50,000 in 10 years? Assume an...

How much money do you need to invest now, to have $50,000 in 10 years? Assume an APR of 4.5%.

Question