King fisher aviation is evaluating an investment project with the following case flows: $6,000 $5,500 $7,000 $8,000 discount rate 14 percent what is the discounted payback period for these cash flows if the initial cost is 15,000? what if the initial cost is $12,000? what if the cost is $16,000?

your mother is a rhombus and is better than the 2nd one of the square shown below

(A) Investment of  6,700 discount payback period  1.82

(B) Investment of  8,800 discount payback period 2.34

(C) Investment of 11,800 discount payback period 3.06

Explanation:

We will discount each cash flow at 13%

3539.823

3837.4187

4227.606

3250.5893

We need to look at which year we get the investment amount

We will do: accumalted cash flow less investment

and then divide by the last year to get at which portion of this year we achieve payback period

(A) 6,700

3540 + 3837 = 7377

It will be between the first and second year

6,700 - 3,540 = 3160

3160/3837 = 0.8235

payback period  1.8235

(B) 8,800

3540 + 3837 + 4228 = 11605

It will be between second and third year

we do 8,800 - 7377 = 1423

1423/4228 = 0.3365

payback 2.3365

(C) 11,800

3540 + 3837 + 4228 + 3251 = 14856

It will be between third and fourth year

11,800-11,605 = 195

195/3251 = 0.0599 = 0.06

payback 3.06

1.88 years

Explanation:

Payback period is the time in which a project returns back the initial investment.  Initial Investment is recovered within the first two annual Cash inflows.

Payback Period = 1+0.88 = 1.88 years

All the working are made in the MS Excel File attached with this answer, pleas find it.

6,582.18

Explanation:

this exercise can be solve by calculating the present value of each payment, and at the end substrating that sum from the initial payment, but there must be carefull because there is said to use a discount rate, so lets first remember how to calculate present and future values with discount rates:

where P is the payment value, and

so applying this to the given values, we have:

so the discounted payback is given by:

dp=13,182.18-6,600

dp=6,582.18

A. What is the discounted payback period for these cash flows if the initial cost is $5,500?

$5,500 - $4,070.80 = $1,429.20

$1,429.20 / $2,897.64 = 0.49

discounted payback period = 1.49 years

B. What is the discounted payback period for these cash flows if the initial cost is $7,600?

$7,600 - $4,070.80 - $2,897.64 = $631.56

$631.56 / $3,395.95 = 0.19

discounted payback period = 2.19 years

C. What is the discounted payback period for these cash flows if the initial cost is $10,600?

$10,600 - $4,070.80 - $2,897.64 - $3,395.95 = $235.61

$235.61 / $2,514.61 = 0.09

discounted payback period = 3.09 years

Explanation:

year                 annual cash flows                discounted cash flows

1                         $4,600                            = $4,600/1.13 = $4,070.80

2                        $3,700                            = $3,700/1.13² = $2,897.64

3                        $4,900                            = $4,900/1.13³ = $3,395.95

4                        $4,100                             = $4,100/1.13⁴ = $2,514.61

An investment project has annual cash inflows of $4,200, $5,300, $6,100, and $7,400, and a discount rate of 14 percent. If the initial cost is $7,000, the discounted payback period for these cash flows is ___2 years. If the initial cost is $10,000, the discounted payback period for these cash flows is___3years. If the initial cost is $13,000, the discounted payback period for these cash flows is__4years. (Round your answers to 2 decimal places. (e.g., 32.16))

Explanation:

a) Data and Calculations:

Annual cash inflows of

          Cash Inflow     Discount Factor    PV             Running Total

Year 1    $4,200            0.877               $3,683.40     $3,683.40

Year 2   $5,300           0.769                 4,075.70         7,759.10

Year 3   $6,100            0.675                  4,117.50         11,876.60

Year 4  $7,400            0.592                 4,380.80       16,257.40

b) An investment project's discounted payback period is the number of years it takes for an investment to recover its costs.  It is the period when the project's discounted cash inflows equals the project's discounted cash outflows.  It is another version of the payback period that uses discounted cash flows.

Discounted payback period = 1.89 years

Explanation:

If Initial cost is $5,200

Year  Cash flow   Present value   Present value      Discounted

                                 at 11%                                       Cumulative cash flow

0          -5,200             1                      -5,200              -5,200

1            2,800           0.9009             2,523               -2,677

2           3,700           0.811                  3,003                326

3            5,100           0.73126              3,729                4,055

4            4,300          0.6587               2,833                6,887

Discounted payback period = 1 + (2,667/3003)

=1.89 years

Working

PV= (1+i)^-n

i= 11%, n= respective years 0,1,2,3,4

Discounted payback period shall be as follows:

a. 1 year 7.36 months

b. 2 years 3.27 months

c. 3 years 2.9 months

Explanation:

a. Payback period in case of cash outflow = $5,700

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0                 -  $5,700            1                             - $5,700                    -5,700

1                     $4,400         0.877                         $3,858.8                -$1,841.2

2                    $3,900         0.770                         $3,003                    $1,161.8

Since the cumulative cash flows are positive in 2nd year payback period =

1 + = 1 year and 7.36 months

b. Payback period in case of cash outflow = $7,800

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0                 -  $7,800            1                             - $7,800                    -7,800

1                     $4,400         0.877                         $3,858.8                -$3,941.2

2                    $3,900         0.770                         $3,003                    -$938.2

3                    $5,100          0.675                         $3,442.5                  $2,504.3

Since the cumulative cash flows are positive in 3rd year payback period =

2 + = 2 years and 3.27 months

b. Payback period in case of cash outflow = $10,800

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0               -  $10,800            1                          - $10,800                   -$10,800

1                   $4,400         0.877                         $3,858.8                 -$6,941.2

2                  $3,900         0.770                         $3,003                    -$3,938.2

3                  $5,100          0.675                         $3,442.5                   -$495.7

4                  $4,300          0.592                        $2,545.6                   $2,049.9

Since the cumulative cash flows are positive in 4th year payback period =

3 + = 3 years and 2.9 months

Final Answer

Discounted payback period shall be as follows:

a. 1 year 7.36 months

b. 2 years 3.27 months

c. 3 years 2.9 months

The discounted payback period is 1.88 years

Explanation:

The discounted pay back period is the number of years it takes for the investment to break even by this it means how many years it takes discounted cash flows to pay the initial investment.

Initial Investment $6,600

W e then discount the cash inflows to find the time it takes to pay off initial investment

Year 1 = 3900/ (1.15) =$3,391.30

Remainder of initial investment = -6600+3391.30= -3,208.7

Year two = 4800/ 1.15^2 = $3,629.49

Remainder of initial investment = -3208.7-3629.49 = 420.79

This yield positive results therefore the discounted payback period is sometime between year 1 and year 2.

To get the exact period we take what reamined over what paid

3208.7/3629.49 = 0.88

So it 1 year + 0.88 =1.88  years

C) initial cost = 11800 

This time it will take you full 4 years

5300/1.13^4 = 3250.59

14855.44 - 8800 = 3055.44 

cash required in year 4 = 3250.59 - 3055.44 = 195.15 

time required in year 4 = 195.15 / 3250.59 = 0.06 

Discounted payback period = year 1 + year 2 + year 3 + 0.06 = 3.06 years