A machine whose life is two years, costs Rs. 110. In each of its life its yield is Rs. 72. What is the expected rate of return on this particular machine ?

To determine the rate of  return, we solve the following equation:

                                       R₁            R₂
                              Cr = _____  + _____
                                     (1+r)       (1+r)²
In this equation :

  Cr = Cost or supply price of the machine, i.e., Rs. 110.
  R₁ and R₂ = Yield in first and second year, i.e., Rs. 72 each  year.
  R = Rate of return.
Substituting the value for Cr, R1 and  R2 in the above equation, we have
                               
                                        72          72
                       Rs. 110 =  ____ + _____       
                                       (1+r)      (1+r)²

Or              110 (1+r)²  =72 (1 + r) +72     
Or       110 (1 + r² +2r) =72 (1 +r) +72
Or    110 +110r² +220r = 72 +72r +72
Or       110r² +148r -34 = 0
Solving this quadratic equation¹ . we get
                                         R = 0.2 or 20%

Thus, the expected rate of return is 20 % . If the market rate of interest is less then the expected rate of return (i.e., 20% ),investor will find it profitable to invest in this project. If, on the other hand, the market rate of interest is greater than the rate of return (i.e., 20%), investor will find it unprofitable to invest in this project. Thus, an investor will choose to invest only if it offers a rate of return higher than the market rate of interest. So the alternative criterion to determine the profitability of investment is the excess of expected rate of return over the market rate if interest,