There were two versions of the test. The questions were identical in the two versions. The tables were different.

- NPV =
-1200000-800000(1.10)
^{-1}+550000*a*_{5|0.10}(1.10)^{-1}= -$31,879.34. Since NPV < 0, the investment is NOT worthwhile. -
*K*_{1}= 60+60/((1.07)^{4}-1) = $295.23.*K*_{2}=*X*+*X*/((1.07)^{8}-1) = 2.3923966*X*.*K*_{1}=*K*_{2}gives*X*= 295.23/2.3923966 = $123.40. Thus you should be willing to pay $123.40 for an eight-year battery.Remark: Many solutions to this found the extra amount $53.40 that should be paid. If you claimed this was the battery price (or did not clarify the point) you lost 2 marks.

- (a) 28000(1-
*d*)^{10}= 8000 so 1-*d*= (2/7)^{0.1}.*B*_{5}= 28000(2/7)^{(0.5)}= $14,966.63.(b)

*R*= (28000-8000)/10 = $2000.00 per year..*B*_{5}= 28000-5(2000) = $18,000.00. - P(at least one dies) = 1 - P(all 20 survive) = 1 - (
*P*(*one**survives*))^{20}= 1-(*l*_{48}/*l*_{18})^{20}. Using the tables, the answer is 0.385 (in one version) or 0.669 (in the other version). - 0.5
^{1/20}= 0.965936329. Let 1+*j*= (1.03)/0.965936329 so*j*= 0.066322871. Then*P*= 45*a*_{20|j}+1000(1+*j*)^{-20}= $767.50 is the price the investor should be willing to pay. - (a) 10000
*D*_{50}/*D*_{40}= $6032.11 (one version) or $5916.28 (other version).(b) 10000(

*l*_{50}/*l*_{40})(1.09)^{-10}= $4150.47 (one version) or $4070.77 (other version). - PV of premiums = PV of benefits so
*R*(*N*_{28}-*N*_{53})/*D*_{28}= 100000*M*_{28}/*D*_{28}. Thus*R*= 100000*M*_{28}/(*N*_{28}-*N*_{53}). This gives $625.90 per year (one version) or $929.92 per year (other version). -
*x**l*_{x}*d*_{x}*p*_{x}*q*_{x}101 1000 200 0.8 0.2 102 800 240 0.7 0.3 103 560 168 0.7 0.3 104 392 196 0.5 0.5 105 196 196 0 1

File translated from T

On 10 May 2001, 16:02.