The State government has purchased $200$ bicycles to replace the current Link Bikes. In

addition, they have also purchased a total of $50$ E$-$scooters to be placed in Gurney Bay,

Straits Quay Promenade, and Queens Waterfront Promenade. The purchase cost of $200$

bicycles is RM $300,000$ and $50$ E$-$scooters is RM$50,000.$ The cost of maintenance of the

bicycles is RM$80,000$ in the first year, RM$90,000$ in the second year and RM$95,000$ in the

third year. The cost of maintenance of the E$-$scooters is RM$30,000$ in the first year,

RM$35,000$ in the second year, and RM$40,000$ in the third year. The benefits of bicycles are

RM $160,000$ in the first year and RM$200,000$ in the second and third years. On the other

hand, the E$-$scooters' estimated benefit is RM $80,000$ in the first year and RM$120,000$ in the

second and third years. At the end of the third year, the bicycles and E$-$scooters can be resold

as second$-$hand for a total of RM$40,000$ and RM $5,000.$ Assume a discount rate of $3\%$ is

used.

a$).$ Calculate the present value of net benefits assuming the benefits are realized at the end

of each of the three years. Also, draw the timeline of benefits and costs.

$(3$ marks$)$

b$)$ Calculate the present value of net benefits assuming that the benefits are realized at the

beginning of each of the three years. Also, draw the timeline of benefits and costs.

$(2$ marks$)$

c$)$ Calculate the present value of net benefits assuming that $50\%$ of the benefits are realized

at the beginning of the year and the balance at the end of the year.

$(3$ marks$)$help