Additional Solutions: Chapter Three: Cash Flow Analysis
Mr Dashwood must find the least value of
1 500 < 100
which is equivalent to finding
Consulting Appendix A, this first occurs when
= 29 years.
If the interest rate is 10%, we come to the end of the table in Appendix A before finding a value of
> 15. We therefore go on to look at the capitalized value of the annuity, which
is 100/0.1, or £1 000. Thus, if he can invest his money at 10%, Mr Dashwood can afford to support his
widowed half-sister indefinitely for a cost equivalent to a single present payment of £1 000.
There are several ways of tackling this.
One way is to convert the bi-annuity to an equivalent annuity:
A1 = A(A/F,i,2)
is the annual payment equivalent to getting a final payment of ¥
at the end of two years.
Then we can convert ¥
to its present worth using a formula we already know:
(Don’t forget that it’s now 2
Another solution is to calculate the effective biennial interest rate,
, from the equation
= (1 +
-1 = 2
and then to use a conversion factor based on
P = A(P/A, j, N)
A third alternative is to construct a formula based on the one at the back of the book,
(P/A, j, N)
and substitute in the value of
, the effective biennial interest rate, as calculated above. This is a correct
solution, but it’s more work. Also, I would advise against using these algebraic formulas, except when
you’re constructing a spreadsheet – evaluating them is more work than looking a number up in the
tables, and there are more opportunities for making a slip.