Product Absorption Rate Formula

Product Absorption Rate Formula

An absorption rate is calculated on the bases of number of unit produced is known as Product absorption rate or absorption rate based on Product. This absorption rate may be calculated by dividing production overheads with total number of units produced (units of different product).

Absorption Rate (Labour Hr) = Production Overhead/Total Products

Product Absorption Rate Formula Example

Total overhead expenditure is $ 300,000 for two products (A, B). Total production of both products is (50,000 units). Calculate Product Absorption Rate

Solution

Absorption Rate (Labour Hr) = Production overhead/Total units Produced

= $ 300,000 (production overhead)/ 50,000 Total Products

= $ 300,000/ 50,000

= $ 6 (product absorption Rate)

Cost of Redeemable Debt

Cost of Redeemable Debt Formula

Cost of redeemable debt is calculated with the help of IRR formula (Internal Rate of return). The formula of IRR has given below

Formula = L +(NPV_L/NPV_H-NPV_L)x (H-L)

R_L= Lower rate of Return

R_H= Higher Rate of Return

NPV_L = NPV with Lower rate of Return

NPV_H= NPV at higher rate of return

Cost of irredeemable debt process has been explained by example;

ABC & Co Quoted	102
Coupon Rate	10%
Tax rate on companies	30%
Maturity	5 years

       Solution

Particulars	Value	Dis. 5%	PV @ 5%	Dis. 10%	PV @ 10
Market Value	102	1	102	1	102
Interest	(7)	4.329	(30.30)	3.791	(26.53)
Redemption Value	(100)	.784	(78.40)	.621	(62.1)
			(6.7)		13.37

      Formula = L +(Nl/Nh-Nl)x (H-L)

      = 5% + (6.7/20.07)(5%)

      =.05+.323(.05)

      =6.65%

Cost of irredeemable Debt

Cost of irredeemable Debt

Irredeemable debt is never paid pack (theoretical concept). Cost of irredeemable debt is calculated by the following formula

Io ( 1-T)/Po

Where,

Io= Interest rate

T= Tax Rate

Po= Market value of debt (Ex interest Price)

 Example

Rate of interests = 9%

Value of Debt= 120

Tax Rate =30%

Solution

Io ( 1-T)/Po

= [ 9(1-30%)]/120

=6.3/120

=5.25% (cost of Debt)

CAPM Formula

CAPM Formula

Cost of equity can be calculated by the CAPM (Capital Asset Pricing Model).This methods takes into account market risk.

CAPM = Rf + βe (Rm-Rf)

Rf= Risk Free Rate

Rm= Market Rate

βe = Equity Beta

Example

Market Rate= 9%

Bank Rate= 12%

Equity Beta= 1.3

Calculate Cost of equity?

Solution

=  12% + 1.3 ( 12%-9%)

=12%+3.9%

=15.9%

Present Value of Compounded Value Formula

Present Value of Compounded Value Formula

Present value of compounded value can be calculated by the following simple formula

Present Value       = Compounded Value/e^rt

E=2.718

r= Rate of interest

t= compounding time

Example

Amount = 10,000

Compound interest= 12%

Period =3 Years

Compounded Value = 10,000x (1+12%)³=14049

Solution

Present Value       = Compounded Value/e^rt

=14,049/(2.718)^(.12)(3)

=14,049/(2.718)^.36

=14,049/1.4333

=9800

Compound Interest Doubling Time Formula

Compound Interest Doubling Time Formula

This following formula is used to calculate the period in which the amount would be doubled using the prevailing interested rate.

Doubling period Formula = ln(2)/r

r= interest Rate

Example

Interest rate =9%

Doubling Period?

Solution

Doubling Period Formula = ln(2)/r

=ln (2)/9%

=ln(2)/.09

=7.70 Years

It takes 7.7 years that an amount would be doubled. for example if 10,000 was invested ,then it would be 20,000 in 7.7 years.

Future Value of Growing Annuity Formula

Future Value of Growing Annuity Formula

There may be a growing series of payment deposited with institution to receive lump sum amount on maturity. Series of payment grow at gradual rate. The future value of such annuity may be calculated by following formula

Annuity Factor =Cx [(1+i)ⁿ-(1+g)ⁿ]

                                  i-g

i= interest Rate

g=Growth rate

n= period

C=Deposited amount

Example

Deposit = 10,000

Growth Rate of deposit = 5%

Interest Rate = 9%

Period =10 Years

Solution

Annuity Factor =10,000x [(1+9%)¹⁰-(1+5%)¹⁰]

                                            9%-5%

=10000 x [2.367 – 1.6288]/.09-.05

=184,550

Future Value of Annuity Due Formula

Future Value of Annuity Due Formula

Future value of annuity is calculated to determine the future value of the series of payment. This concept is widely used in insurance company.

Annuity Factor =Cx [(1+i)ⁿ-1] x (1+r)

                              i

Example

Amount Deposited= 2000

Period = 5 Years

Interest Rate =9%

Solution

Annuity Factor =C x [(1+i)ⁿ-1] x (1+r)

                               i

= Cx [(1+9%)⁵-1] x (1+9%)

           9%

=5.984 x 1.09

=6.5233

=6.5233 X 2000

=13,047

MIRR Formula

MIRR Formula

IRR use the same rate for reinvestment of fund, which is not practical. Therefore MIRR concept has been introduced, which uses the cost of capital as reinvestment.

MIRR = n√A/B

n= life of project

A= Recovery phase Cash flows

B= Investment phase Cash flow

Example

Year               Cash Flows

0                          (100,000)

1                            (20,000)

2                             50,000

3                             50,000

4                             40,000

5                            (20,000)

IRR is 12% and discount Rate is 8%, Calculate MIRR?

Solution

Investment Phase discounting

Year       Cash Flows      Discount              PV

0               (100,000)          1                      (100,000)

1                (20,000)          (1.08)^-1                   (18,518)

Total                                                           118,518

Recovery Phase flows

Year     Cash Flows       Discount         PV

2                  50,000          (1.08)³           62986

3                  50,000          (1.08)²           58320

4                  40,000           (1.08)¹          43200

5                  (20,000)          1                (20000)

                                                               144,506

MIRR = n√A/B -1

= 5√144,506/118518

=4.04%

IRR Formula

IRR Formula

IRR can be calculated with the help of following formula. It is important that IRR is an estimated calculation only. IRR tell us about the rate, where NPV will become zero. IRR is return of the project, if such return is greater than expected return, then project is to be selected, otherwise rejected.

R_L+ {  NPV_L          } x (R_H-R_L)

         NPV_L-NPV_H

R_L= Lower rate of Return

R_H= Higher Rate of Return

NPV_L = NPV with Lower rate of Return

NPV_H= NPV at higher rate of return

Example

Year

0     100,000

1      30,000

2      30,000

3      35,000

4      15,000

Calculate IRR?

Solution

We assume that IRR falls between 10% & 15%.

Year                  Discount           PV @10%     Discount           PV @ 15%

0     100,000         1                   (100,000)                           (100,000)

1      30,000       (1+10%)^-1          27,272        (1+15%)^-1        26,086  

2      30,000       (1+10%)^-2          24,793       (1+15%)^-2        22,684   

3      35,000       (1+10%)^-3          26,296       (1+15%)^-3         23,013   

4      32,000       (1+10%)^-4          21,856        (1+15%)^-4        18,296

NPV                                             217                                (9,921)            

R_L+ {  NPV_L          } x (R_H-R_L)

         NPV_L-NPV_H

= 10% + [ 217/(217- (-9921)]x [ 15%-10%)

=10%+ [217/10,138] x [5%]

=10.10%

Money Interest Rate Formula

Money Rate Formula

Money Rate can be calculated from the real rate and inflation rate by fisher effect. It is important to note that money rate is roughly a sum of inflation rate & real rate.

(1+m) = (1+i)(1+r)

m=money rate

i= inflation rate

r= real rate

Example

Inflation rate in country = 5%

Real rate in country = 6%

Money Rate=?

Solution

(1+m) = (1+i)(1+r)

Money rate = (1.05)(1.06)-1

= (1.113)-1

=.071

=11.3%

Simple Interest Formula

Simple Interest Formula

Future value is calculated by the following simple formula

Future value = P ( 1+ Rn)

R= rate of interest

N = number of period

P = Present value

Simple Interest Formula Example

Bank is offering a simple rate of interest 12% (p.a) . Mr. A wants to deposit $ 25,000 today. How much amount Mr. A will received in 4 years?

Solution

= $ 25,000 (1+ .12x4)

=$ 25,000 x 1.48

=37,000

In simple interest the interest in not re invested therefore the interest amount remains same for each year.

Real Interest Rate Formula

Real Interest Rate Formula

Real rate does not include inflation rate, and can be calculated from money rate and inflation rate by using fisher effect formula. it is important to note that real rate is roughly money rate minus inflation rate, but exact rate can be calculated by fisher effect.

 (1+m) = (1+i)(1+r)

Re arrange formula

r         = (1+m)   -1

              (1+i)

m=money rate

i= inflation rate

r= real rate

Example

Prevailing Inflation rate = 8%

Money Rate in market = 12%

Money Rate=?

Solution

r        = (1+m)   -1

              (1+i)

r       = (1+12%) -1

              (1+8%)

=3.7% (Real Rate)

Interest Cover Formula

Interest Cover Formula

Interest cover ratio is calculated to know the company ability to pay interest. Interest cover ratio is calculated by following equation. Interest cover is expressed in term No of times. In other word it explains how much profit is available to pay interest.

Interest Cover =    Profit before Interest & Tax

                                      Interest

Example

Mr. Ali khan reported a Profit of $ 800,000 & interest is payable on debenture amount 10 million @ 4%. How much profit is available to pay interest?

Solution

Interest Cover =    Profit before Interest & Tax

                                        Interest

= $ 800,000/$ 400,000

=2 times

Equal Annual Return Formula

Equal Annual Return Formula

Equal annual return from a project may be calculated by applying annuity Factor. This concept has been explained with an example

Annual Return =         = Present Cash flow

                            Annuity Factor

  

Example

Project cost = 90,000

Term of project = 5 Years

Rate of Return = 12%

Calculate equal return from project?

Solution

Annuity Factor

= 1-(1.12)^-5

        .12

=3.6044

Annual Return

Annual Return =         = Present Cash flow

                        Annuity Factor

  

= 90,000/3.6044

=24,969

Effective Interest Rate Formula

Effective Interest Rate Formula

Effective Interest Rate is calculated with the help of following formula.

1+R= (1+i) ⁿ

R= Rate of Interest

I= Rate of interest for period (months, quarter, semiannual)

n= Number of periods (months, quarter, semiannual) in year

Example

A got a credit card from a reputable bank and bank offered him a 3% interest per months. Credit card amount was $ 10,000. Calculate the interest for the year?

R = (1+i) ⁿ-1

= (1.03)¹²-1

=1.4257-1

=.4257

= 42.57%

Interest amount = 10,000 x 42.57 %

=$ 4,257

Purpose of effective Interest Rate

Effective interest rate gives you annual interest cost and an effective tool to measure the different financial product. Effective interest rate takes into account the periodical compounding effect.

Compound Interest Formula

Compound Interest Formula

Compound interest is quite different from the simple interest. In compound interest the interest is not received by the investor each year , instead such interest is reinvested each year , therefore investor earn interest not only on principal amount but also on interest earn till the maturity.

Future value = P (1+r) ⁿ

P= Present Value

r= rate of interest

n= number of period

Example

Bank Deposit= 150,000

Rate of interest = 8%

Solution 

Future value = P (1+r)ⁿ

= $ 150,000(1.08)³

=$ 188,956.8

Interest for three years = future value – present value

= 188,956.8-150,000

=38,956.8

Future Annuity Present Value Formula

Future Annuity Present Value Formula

Present value of Future annuity may be calculated by the following formula

C x (Annuity Factor) x Discount Factor

Future Annuity Example

Annuity 50,000 ( 6-8)

Discount Rate = 5%

Solution

In first place we would determine the time line

0	1	2	3	4	5	6	7	8
						50,000	50,000	50,000

1.    Calculate the annuity at year 5

= 1-(1.05)^-3

        .05

=2.723

= $ 50,000 x 2.7232

=136160

2.    Discount the present value at year zero

0	1	2	3	4	5
					136,160

$ 136,160 x (1+.05)^-5

=$136,160 x .7835

=106,681

Tip of future annuity

One your discount for term of annuity i.e. 3 Year

Discount further for year Zero i.e. 5 Year

Total Discounting 3+5 =8 Years

Method 2

Annuity Factor 8 year      6.4632

Annuiy Factor 5 Year       4.3294

Annuity factor (6-8)         2.1338

50,000 x 2.1338

=106,690