# Confused in using the salvage value in Rate of Return.

I am trying to solve a rate of return question from the book Engineering Economics by R. Paneerselvam. In that particular problem I am given a salvage value along with other factors. Following are the factors:

i) Initial cost

ii) Annual incremental revenue

iii) Life

iv) Life-end Salvage value (Rs.)

Now when salvage value is not given we use the following formula:

$$PW_n(i) = -P + A(P/A,i,n)$$

Now how will this formula be modified when salvage value is also added? I mean what factor will be introduced alongside the Salvage value?

• I´ve noticed that I didn´t discounted the sum of the annuities. I´ve made an edit of my answer. Jul 4 '19 at 15:16

To obtain the present value of the salvage value ($$S$$) you discount the value of the salvage $$n$$ times. Therefore the whole formula is
$$PV_n(i)=-P+A\cdot \frac{(1+i)^n-1}{i\cdot (1+i)^n}+\frac{S}{(1+i)^n}$$
• the one you used in the formula is P/F. $S(F/P) = S(1+i)^n$ Jul 4 '19 at 22:54
• @AhmadQayyum We get the salvage value (S) after $n$ periods. To obtain the present value we have to discount it $n$ times. Jul 4 '19 at 22:59