Question

Dl CHaranda Final-May 16, 2019 Name and signature: Manolo Felician 0 1. You have 1.5 hours to complete the exam, or equivalently 45 minutes for each exam page. 2. You can only use your (financial) calculator. Only answers inside the boxes under each question will be graded. 4. You have a list of formulas on the 3rd page, and you can use the 4th page for extra computations 1) The following two questions are independent from each other. a) Your factory has been offered a contract that would last for 2 years, with cash flows 6 million per year. Your upfront setup costs would be $9 million now. Show that the IRR is 2 1.53%. In addition, if your discount rate is 10%, dotheIRR and NPV rules agree? b) You need to decide how to allocate space in your production facility. You are considering the following 3 contracts. Contract A with NPV million and 100% use of facility; Contract B with NPV $4 million and 50% use of facility; and Contract C with NPV $3 million and 50% use of facility, what should you do? 2) Queens Corporation (QC) has the following expected dividends per share: $1 in one year, $2 in two years, and $3 in three years. After that, its dividends are expected to grow at 10% per year forever (so that year 4's dividend will be 10% more than $3 and so on). QC's equity cost of capital is 15%. a) Show that we expect the stock price to be $66.00 at the beginning of the 4h year What is the current stock price? Hint: Discount the 3 dividends and the price in o) b)

Answer 1

Question 1)

a) Calculation of IRR

IRR is the rate at which all the present value cash inflows are equal to the present value of cash outflows.

There is one cash inflow of $9 million now and two cash flows of $6 million each in the upcoming two years.

You can simply input (-9,000,000) in Year 0's cash flow. The minus sign signifies a cash outflow. Then input 6,000,000 in Year 1 and Year 2. Then using your financial calculator, compute IRR. The result will be 21.5250437% or 21.53%.

If you are having difficulties using your financial calculator, you can solve for i% in the following formula by iteration:

Present Value of Cash Inflows = Present Value of Cash Outflows at i%

or, 9,000,000 = 6,000,000/(1+i%) + 6,000,000/(1+i)^2

Following this method will also yield you the same result of IRR of 21.53%.

Calculation of NPV

NPV is the Present Value of cash inflows net of present value of cash outflows.

You can either using the same steps as IRR to compute NPV in your financial calculator after inputting the interest rate at 10%. You can simply input (-9,000,000) in Year 0's cash flow, then input 6,000,000 in Year 1 and Year 2. Using a discount rate of 10% in your financial calculator, compute NPV. The answer will be $1,413,223.141.

If you have difficulty doing so, calculate NPV using its formula:

NPV = Present Value of cash Inflows - Present Value of cash Outflows at the given discount rate

Using the above formula, we calculate NPV as:

YEAR	CASH FLOW	Formula for Present Value	Present Value
0	-$9 million	-$9 million/(10%)^0	-$9 million
1	$6 million	$6 million/(1+10%)^1	$5,454,545.455
2	$6 million	$6 million/(1+10%)^2	$4,958,677.686
Total Present Value			$1,413,223.141

Using the above method or your financial calculator will yield the same result of $1,413,223.141.

Conclusion

Since, the Net Present Value is positive, we accept the project. The IRR (21.53%) is greater than the cost of capital (10%) and so the IRR criteria permits acceptance of the project. Therefore, at 10% level of discount, both NPV and IRR rules agree.

b) The NPV rule states that if there are multiple contracts, we always choose the one with the highest NPV. Since, different combinations are possible, we will consider all the combinations and choose the combination that yields the highest NPV and uses the entire facility to avoid under-utilization of resources.

Formula: NPV of a combined contract = sum of NPVs of individual contracts

Possible Combinations and their NPV at 100% use of facility:

Combination	Use of facility	Net Present Value
Contract A	100%	$5 million
Contract B and C	100% (50% + 50%)	$7 million ($3 million + $4 million)

Therefore, I advice allocating 50% space to contract B and 50% space to contract C to yield an NPV of $7 million, which is higher than the NPV of $5 million if 100% space is allocated to Contract A.

Question 2)

a) Using the Gordon Growth Model of dividend discounting, we compute the stock price at the beginning of the fourth year. The formula of Gordon Growth Model is:

Price = Dividend in the year end / (Cost of equity capital - Perpetual Growth rate)

For Year 4, the dividend at year beginning is $3. The dividend at year end is:

Dividend at beginning of the year * (1+Growth rate) = $3 * (1+10%) = $3.30

Cost of equity capital is 15% and the perpetual growth rate is 10%.

Now, we use the stated formula to compute Price of the stock at the end of Year 4:

Price = $3.30 / (15%-10%) = $66

b) For calculating the current price, we will discount back all the future cash flows to the present at the cost of equity capital.

Formula for Present Value : Present Value = Cash Flow / (1+Interest Rate)^Time period

Year	Cash Flow	Formula	Present Value
1	$1	$1 / (1+15%)	$0.892857143
2	$2	$2 / (1+15%)^2	$1.512287335
3	$3 + $66 = $69	$69 / (1+15%)^3	$45.36862004
Total Present Value			$47.75047259

Note: The value of Cash flow in the 3rd is the sum of the dividend of $3 received during that year and the price of the stock at that time (Beginning of Year 4 = End of Year 3).

Therefore, the current price of the stock is $47.75.