In which cases do we need to manipulate the Real Equation of value formula?

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asked Jan 14, 2017

Question 2 and 4 from Tutorial 3 both require us to use the Real Equation of value.
However, Question 2 requires us to manipulate the formula; and Question 4 requires us to make use of the formula without any manipulation. Why is that?
How do we know that we need to manipulate the formula?

For Q2 the first coupon has a known $$Q(t_{1} - LAG)$$ and so you cannot estimate it as $$Q(t_1 - LAG) = Q(t_L)(1 + \alpha)^{t_1 - LAG - t_L}$$. Instead you use the known value 8 months before purchase. But for Q4 any value of $$Q(t)$$ after purchase date $$t_{0}$$ must be estimated.