Here is the ORIGINAL data of the Sporthotel problem: 1. Projected outflows First
ID: 2783995 • Letter: H
Question
Here is the ORIGINAL data of the Sporthotel problem:
1. Projected outflows First year (Purchase Right, Land, and Permits) $1,000,000 Second Year (Construct building shell $2,000,000 Third Year: (Finish interior and furnishings) $2,000,000 TOTAL $5,000,000
2. Projected inflows If the franchise is granted hotel will be worth: $8,000,000 when it opened If the franchise is denied hotel will be worth: $2,000,000 when it opened. The probability of the city being awarded the franchise is 50%.
Suppose that everything is the same as in that problem except one thing: the worth of the hotel, should the city be awarded the franchise, is not $8 million but some unknown smaller number. What must the new worth of the hotel when the franchise is granted be in order for the NPV of the Sporthotel project to be equal to exactly zero?
Explanation / Answer
Given Data:
Particulars
Amount
Projected Outflows for the first Year:
$ 10,00,000.00
Projected Outflows for the Second Year:
$ 20,00,000.00
Projected Outflows for the Third Year:
$ 20,00,000.00
Total
$ 50,00,000.00
Projected Inflows
When Franchise Granted
When Franchise is Denied
8000000
2000000
Probabability of city being awarded as franchise
50%
ANSWER
(1) At Internal rate of Return(IRR) the Net present value (NPV) Stands Zero i.e.,
(2) At IRR point of rate Present value of Cashinflows = Present value of cash outflows
In the Given Problem, the point is Net worth of the hotel when franchise is granted when Net Present value(NPV) is Zero
Here we can consider the points as said above (2)
I.e., Present value of Cashoutflows for Sport hotel = Present value of Cash inflows for Sport hotel ( when Franchise is Granted)
** Assume 10% is the Rate of Return over the Project
Year
Cash flows
Present value factor @10%
Amount
1
$ 10,00,000.00
0.909090909
$ 9,09,090.91
2
$ 20,00,000.00
0.826446281
$ 16,52,892.56
3
$ 20,00,000.00
0.751314801
$ 15,02,629.60
Total cash Outflows
$ 40,64,613.07
In order to comply with the problem and make NPV as Zero , The Present valu of Net Worth of the Sport hotel should be 4064613.07
So in order to know the cashflows , we need to calculate reversely for Inflows
Cashinflows =
Present value of cash in flows
Present value factor for three years (accumulated)
=
4064613.07
.9091+.8264+.7513
4064613.07
2.4869
Net Worth of the Sport hotel ( Cashinflows) in order to maintain NPV at Zero Value
1634441.086
Given Data:
Particulars
Amount
Projected Outflows for the first Year:
$ 10,00,000.00
Projected Outflows for the Second Year:
$ 20,00,000.00
Projected Outflows for the Third Year:
$ 20,00,000.00
Total
$ 50,00,000.00
Projected Inflows
When Franchise Granted
When Franchise is Denied
8000000
2000000
Probabability of city being awarded as franchise
50%
ANSWER
(1) At Internal rate of Return(IRR) the Net present value (NPV) Stands Zero i.e.,
(2) At IRR point of rate Present value of Cashinflows = Present value of cash outflows
In the Given Problem, the point is Net worth of the hotel when franchise is granted when Net Present value(NPV) is Zero
Here we can consider the points as said above (2)
I.e., Present value of Cashoutflows for Sport hotel = Present value of Cash inflows for Sport hotel ( when Franchise is Granted)
** Assume 10% is the Rate of Return over the Project
Year
Cash flows
Present value factor @10%
Amount
1
$ 10,00,000.00
0.909090909
$ 9,09,090.91
2
$ 20,00,000.00
0.826446281
$ 16,52,892.56
3
$ 20,00,000.00
0.751314801
$ 15,02,629.60
Total cash Outflows
$ 40,64,613.07
In order to comply with the problem and make NPV as Zero , The Present valu of Net Worth of the Sport hotel should be 4064613.07
So in order to know the cashflows , we need to calculate reversely for Inflows
Cashinflows =
Present value of cash in flows
Present value factor for three years (accumulated)
=
4064613.07
.9091+.8264+.7513
4064613.07
2.4869
Net Worth of the Sport hotel ( Cashinflows) in order to maintain NPV at Zero Value
1634441.086