Bond Duration Formula

Bond Duration Formula

Average Recovery period of investment in bond is technically known is bond duration. For calculating bond duration period of investment is used as weighting and multiplied with return.

Formula for bond duration

Bond Duration =     ∑r x w

                               ∑r

r= return

w= period of return

Bond duration purpose

Bond duration and market price of the bond has close relationship. high duration bond are more price sensitive than low duration bond. High duration bond will take more pressure for a fall in market price of bond.

Example

Year      Return

1                  20

2                  20

3                120

Solution

Year (w)     Return(r)        Return x period (r x w)

1                          20                         20

2                          20                         40

3                        120                       360

Total                 160                       420

= 420/160

= 2.62 Year

Project Duration Formula

Project Duration Formula

Duration of project is average time period of return from the project. Duration of project focuses more on the recovery of expected return than initial investment.

= ∑r x w/ ∑ r

Where

w= period

r= Present value of return

Duration of Project Assumption

1.    initial investment (negative cash flows are ignored)

2.    Takes into account all return from the project

3.    Subsequent negative cash flows are accounted for

4.    Period of return is used for weighting

Example

Year            Cash flows

0                 400

1                 200

2                 200

3                 300

Rate of return is 10%

Solution

Year (w)          Return             Discount          PV (r)     Return x period (r x w)

1                              200                   (1.1)^-1               182                      182

2                              200                   (1.1)^-2               165                      330

3                             300                    (1.1)^-3               225                      675

Total                                                                          572                      1187

= 1187/572

= 2.07 Years

Discounted Payback period Formula

Discounted Payback period Formula

Discounted payback period takes into time value of money. Payback period was widely criticized for its time value ignorance limitation. By introducing discounted payback period this limitation can be removed.

Example

Year 0          200,000

Year 1          80,000

Year 2          70,000

Year 3          80,000

Year 4          60,000

Discount rate 20 Calculate discounted payback period

Solution

Year             Amount             Discount Rate            PV             Cumulative PV

Year 0          200,000              1                      (200,000)

Year 1          80,000              (1+20%)^-1              66,667               133,333

Year 2          70,000              (1+20%)^-2              48,611                84,722

Year 3          80,000              (1+20%)^-3              46,296               38,426

Year 4          90,000              (1+20%)^-4              43,402               (4976)

A + B/C

A= previous year when cumulative value become negative

B= Cumulative value of last year

C= PV of year in which value become negative

3 + 38426/43402

=3.885 Years

Payback Period Formula

Payback Period Formula

Payback period of a project can be calculated by the following formula.

A + B/C

A= previous year of year in which cumulative cash flow became negative

B= Cumulative Balance at year A

C= Total amount recover in a year (year in which total recovery took place)

Example

0          1200

1          400

2          500

3          400

Solution

Investment		($ 1200)
Year 1	$ 400	$ 800
Year 2	$ 500	$ 300
Year 3	$ 400	($ 100)

A = 2 Year

B= $ 300

C= $ 400

Put value in formula = A+ B/C

= 2 + 300/400

=2.75 Years

Annuity Payback Period Formula

Annuity Payback Period Formula

Annuity payback period can be calculated by the following formula

Payback period = Initial Investment / Cash Flows

Example

Initial investment = 120,000

Equal Cash flows = 25000

Solution

Payback period = Initial Investment / Cash Flows

= $120,000/$25000

= 4.8 Years