Question

Problem 3-9
Current and Quick Ratios

The Nelson Company has $1,755,000 in current assets and $650,000 in current liabilities. Its initial inventory level is $325,000, and it will raise funds as additional notes payable and use them to increase inventory.

1. How much can Nelson's short-term debt (notes payable) increase without pushing its current ratio below 2.1? Round your answer to the nearest cent.
2. What will be the firm's quick ratio after Nelson has raised the maximum amount of short-term funds? Round your answer to two decimal places.

Problem 3-10
Times-Interest-Earned Ratio

The Morris Corporation has $300,000 of debt outstanding, and it pays an interest rate of 10% annually. Morris's annual sales are $1.5 million, its average tax rate is 35%, and its net profit margin on sales is 4%. If the company does not maintain a TIE ratio of at least 6 to 1, its bank will refuse to renew the loan and bankruptcy will result. What is Morris's TIE ratio? Round intermediate calculations to two decimal places. Round your answer to two decimal places.

Problem 4-10
Present and Future Values of Single Cash Flows for Different Interest Rates

Use both the TVM equations and a financial calculator to find the following values. Round your answers to the nearest cent. (Hint: Using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

1. An initial $700 compounded for 10 years at 3.2 percent.
   $   
2. An initial $700 compounded for 10 years at 6.4 percent.
   $   
3. The present value of $700 due in 10 years at a 3.2 percent discount rate.
   $   
4. The present value of $700 due in 10 years at a 6.4 percent discount rate.
   $  

Problem 4-14
Uneven Cash Flow Stream

1. Find the present values of the following cash flow streams. The appropriate interest rate is 6%. Round your answers to the nearest cent. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator's cash flow register, you must enter CF₀ = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the Chapter 4 Tool Kit.)

   Year	Cash Stream A	Cash Stream B
   1	$100	$300
   2	400	400
   3	400	400
   4	400	400
   5	300	100

   
   Stream A $   
   Stream B $   
2. What is the value of each cash flow stream at a 0% interest rate? Round your answers to the nearest cent.
   Stream A $   
   Stream B $  

Problem 4-25 Repaying a Loan

While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 10.60%. If Mary repays $1,500 per year, how long (rounded up to the nearest year) will it take her to repay the loan?

year(s)

Problem 4-26
Reaching a Financial Goal

You need to accumulate $10,000. To do so, you plan to make deposits of $1,200 per year - with the first payment being made a year from today - into a bank account that pays 8.58% annual interest. Your last deposit will be less than $1,200 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole number.
year(s)

How large will the last deposit be? Round your answer to the nearest cent.
$

Answer 1

3-9

Current ratio is calculated as:

$Current\: ratio =\frac{Current\: assets}{Current\: liabilities}$

If the firm raises additional short term loans, its current liabilities will go up. The maximum amount of short term loans that it can raise can be calculated using the above formula and substituting 2.1 as the current ratio:

$2.1 =\frac{1,755,000}{650,000 + increase\: in\: short\: term\: debt}$

so, maximum possible increase in short term debt = $185,714 (rounded off)

Quick ratio is calculated as:

$Quick\: ratio =\frac{Liquid \:Current\: assets}{Current\: liabilities}$

here, liquid current assets is nothing but current assets minus inventory. Inventory is excluded as it is not regarded as a highly liquid asset.

Calculation of quick ratio:

$Quick\: ratio =\frac{1,755,000 - 325,000}{650,000 + 185,714}$

Therefore, quick ratio = 1.71

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3-10

Times interest earned ratio gives a sense of how well positioned a company is to be able to pay its interest expenses. It is calculated using the formula:

$times\: interest\:earned=\frac{Income\: before\: interest\: and\: taxes}{interest \:expense}$........................(1)

In the above formula income before interest and taxes is taken instead of net income because interest is paid before paying taxes. In order to calculate this figure, we need to calculate tax expense and interest expense.

Interest expense = interest rate * total debt outstanding

so, Interest expense = 10% * $300,000 = $30,000

Now, it is given that the net profit margin of this company is 4% of sales. So, its net income can be calculated as:

Net income = 4% of $1.5 million = $60,000

In order to calculate earnings before taxes, we can use the below relation:

Net income = Earnings before taxes * (1 - tax rate)

Substituting the values and solving for Earnings before taxes we get,

$Earnings\: before\:taxes= \frac{Net\: Income}{1-tax\: rate}$

or, Earning before taxes =  $92,307.7

Now, Times interest earned can be calculated using eq (1)

$times\: interest\:earned=\frac{92,307.7-30,000}{30,000}$

or times interest earned = 2.08

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4-10

The TVM equation is given as:

$Future\: value = Present \: value * (1+interest)^{no. of periods}$

a.

Substituting $700 as present value, 3.2% as interest and 10 years as no. of periods, we get

$Future\: value = 700 * (1+0.032)^{10}$

or, future value = $959

b.

Same procedure, just interest rate is 6.4% this time

$Future\: value = 700 * (1+0.064)^{10}$

Future value = $1,302

c.

Here, we are given future value and we have to calculate present value. Substituting $700 for future value, 3.2% for interest rate and 10 for period, we get:

$Present\: value = \frac{700 }{(1+0.032)^{10}}$

Present value = $511

d.

Same procedure

$Present\: value = \frac{700 }{(1+0.064)^{10}}$

Present value = $376

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4-14

a.

To calculate total present value, each cash flow has to separately discounted using its respective period. The formula used is:

$Present\: value = \frac{Cash\: Flow }{(1+interest \:rate)^{period}}$

So for cash stream A, first cash flow will be discounted as:

$PV_{1} = \frac{100}{(1+0.06)^{1}}=94.3$

Similarly all other cash flows are calculated by substituting their respective periods. So, for 2nd cash flow, period =2 and so on. Then finally total present value is calculated by summing the present values of all individual cash flows. Calculations are shown below:

b.

When interest rates are 0%, the total present value is simply the sum of all cash flows as no interest is being paid.

So, present values of both stream A and B is $1600.

4-25

The formula used for this equation is the present value of annuity formula given as:

$PV=P\left [ \frac{1-(1+r)^{-n}}{r} \right ]$

where P is the annual payment, r is the interest rate and n is the no. of periods. Substituting $12,000 for PV, $1,500 for P and 10.60% for r, we can solve for n:

$12,000=1,500\left [ \frac{1-(1+0.106)^{-n}}{0.106} \right ]$

On, simplification we get

$0.152=(1.106)^{-n}$

taking the logarithm we have

$\log _{1.106}0.152=-n$

or n= 19 years (rounded off)

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4-26

The formula to be used here is the future value of annuity formula given as:

$FV=P\left [ \frac{(1+r)^{n}-1}{r} \right ]$

Substituting $10,000 for FV, $1,200 for P and 8.58% for r, we can solve for n:

$10,000=1,200\left [ \frac{(1+0.858)^{n}-1}{0.858} \right ]$

On simplification, we get

$8.15=(1.858)^{n}$

Again taking log and solving for n, we get:

n=3 years (rounded off)

Also since the first payment is a year from now, it will take 4 years to reach the goal.